Winners Institute Indore.

Maths With Aditya Patel Sir

Mensuration (2D & 3D)

Class Study Sheet by Aditya Patel Sir

If a diagonal of a square is 30 cm, what is its (in KM )

area? The radius of a wheel is 3.5 m. If the wheel is
(a) 450 (b) 300 rotated 3500 times, then how much distance
(c) 400 (d) 350 will it cover (in KM )?
(a) 77 (b) 800
(c) 770 (d) 77000
By- Aditya Sir Winners Institute

The length and width of a rectangle is 5: 4 if

its area is 8000 square meters. Find the A wheel covers 198 km in 3000 round. Finds
perimeter? its radius?
(a) 350 (b) 380 (a) 10.5 (b) 3.5
(c) 360 (d) 450 (c) 10 (d) 12.5

There is a rectangular ground of 50 m in A Cow with a 7m long rope is tied in a middle

length and 40 m in width, on the inside of of a field having 30m length and 25m width.
which a 5 m wide road, then what is the area Then find the area that cow cannot eat?
of the road? (a) 569 (b) 596
(a) 800 (b) 2000 (c) 560 (d) 154
(c) 1000 (d) 1200

Between a square of perimeter 44 cm and a

circle of circumference 44cm, which figure
has larger area and by how much?
There is a rectangular ground of 60 m in
(a) Square, 33cm2
length and 40 m in width. On the outside of
(b) Circle, 33 cm2
which a 5 m wide road, then what is the area
(c) Both have equal area
of the road?
(d) Circle, 495 cm2
(a) 1000 (b) 1100
(c) 800 (d) 1500

The perimeter of a square and a circular field

are same. If the area of the circular field is
There is a rectangular plain of 60 meters in length 3850 sq meter. What is the area (in m2) of the
and 40 meters in width, in the middle of the square?
parallel field there is a 2m wide road, then the (a) 4225 (b) 3025
area of the road is known? (c) 2500 (d) 2025
(a) 180 (b) 200
(c) 194 (d) 196
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4 √𝟐 (a) 1520 m2 (b) 2420 m2

(c) 2480 m2 (d) 2520 m2

The diagonal of a square is 4 √𝟐cm. The

diagonal of another square whose area is
double that of the first square is:
(a) 8√𝟐 cm (b) 16 cm The length of a rectangular hall is 5m more
than its breadth. The area of the hall is 750m2
(c) √𝟑𝟐 cm (d) 8 cm
The length of the hall is:
(a) 15 m (b) 22.5 m
(c) 25 m (d) 30 m

The length of a rectangular garden is 12

meters and its breadth is 5 metres. Find the
length of the diagonal of a square garden
A copper wire is bent in the shape of a
having the same area as that of the
square of area 81 cm2. If the same wire is
rectangular garden?
bent in the form of a semicircle the radius (in
(a) 2 √𝟑𝟎 m (b) √𝟏𝟑 m 𝟐𝟐
cm) of the semicircle is (𝒕𝒂𝒌𝒆 𝝅 = 𝟕 )
(c) 13 m (d) 8√𝟏𝟓 m
(a) 126 (b) 14
(c) 10 (d) 7

8cm

The area of the square in scribed in a circle

A wire when bent in the form of a square
of radius 8 cm is.
encloses an area of 484 sq. cm. What will be
(a) 256 sq. cm (b) 250 sq. cm
the enclosed area when the same wire is
𝟐𝟐
(c) 128 sq. cm (d) 125 sq. cm
bent into the form of a circle? (𝑻𝒂𝒌𝒆 𝝅 = )
𝟕
(a) 125 cm2 (b) 230 cm2 32cm
(c) 550 cm2 (d) 616 cm2 8cm

A A kite is in the shape of a square with a

diagonal 32 cm attached to an equilateral
B triangle of the base 8 cm approximately how
much paper has been used to make it?
(𝑼𝒔𝒆 √𝟑 = 𝟏. 𝟕𝟑𝟐)
(a) 539.712 cm2 (b) 538.721 cm2
A took 15 sec. to cross a rectangular field (c) 540.712 cm2 (d) 539.217 cm2
diagonally walking at the rate of speed
52m/min and B took the same time to cross
the same field along its sides walking at the
rate speed 68 m/min. The area of the field is:
(a) 30 m2 (b) 40 m2
2
(c) 50 m (d) 60 m2 How many tiles, each 4 decimetre square will
be required to cover the floor of a room 8 m
long and 6 m broad?
(a) 200 (b) 260
(c) 280 (d) 300
The difference between the length and
breadth of a rectangle is 23 m. If its perimeter
is 206 m, then its area is.
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In a triangular field having sides 30m, 72m

and 78m, the length of the altitude to the side
measuring 72m is.
(a) 25 cm (b) 28 cm
The area of the ring between two concentric
(c) 30 cm (d) 35 cm
circles, whose circum ference are 88 cm and
132 cm is.
(a) 78 cm2 (b) 770 cm2
2
(c) 715 cm (d) 660 cm2

The circumference of a circle is 11 cm and

the angle of a sector of the circle is 600. The
𝟐𝟐
area of the sector is.(𝒖𝒔𝒆 𝝅 = 𝟕 )
𝟐𝟗 𝟐𝟗
(a)𝟏 𝟒𝟖 𝒄𝒎𝟐 (b) 𝟐 𝟒𝟖 𝒄𝒎𝟐
A path of uniform width sur rounds circular 𝟐𝟕 𝟐𝟕
park the difference of internal and external (c) 𝟏 𝟒𝟖 𝒄𝒎𝟐 (d) 𝟐 𝟒𝟖 𝒄𝒎𝟐
circumference of this circular path is 132
𝟐𝟐
metres. Its width is:(𝑻𝒂𝒌𝒆 𝝅 = 𝟕 )
(a) 22 m (b) 20 m 𝟏𝟐𝟏√𝟑
(c) 21 m (d) 24 m

A copper wire is bent in the form of an

equilateral triangle and has area 𝟏𝟐𝟏√𝟑 cm2
If the same wire is bent into the form of a
circle the area (in cm2) enclosed by the wire
𝟐𝟐
Four equal sized maximum circluar plates is.(𝑻𝒂𝒌𝒆 𝝅 = 𝟕 )
are cut off from a square paper sheet of area (a) 364.5 (b) 693.5
784 sq. cm. The circumference of each plate (c) 346.5 (d) 639.5
𝟐𝟐
is. (𝑻𝒂𝒌𝒆 𝝅 = 𝟕 )
(a) 22 cm (b) 44 cm
(c) 66 cm (d) 88 cm

Three circles of diameter 10 cm each are

bound together by a rubber band as shown
in the figure.
The length of the rubber band (in cm) if it is
The area of a circle is increased by 22cm2, if
strectched is.
its radius is increased by 1 cm. The original
radius of the circle is
(a) 6 cm (b) 3.2 cm
(c) 3 cm (d) 3.5 cm

(a) 30 (b) 30 + 10 𝝅
(c) 10 𝝅 (d) 60 + 20 𝝅
A circle is inscribed in an equatilateral
triangle of side 8 cm. The area of the portion
between the triangle and the circle is
(a) 11 cm2 (b) 10.95 cm2
2
(c) 10 cm (d) 10.50 cm2
The perimeter of a triangle is 40 cm and its
area is 60 cm2. If the largest side measurres
17 cm, then the length (in cm) of the smallest
side of the triangle is.

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(a) 4 (b) 6
(c) 8 (d) 15

√𝟑
A horse is tied to a post by a rope. If the
If the numerical value of the perimeter of an horse moves along a circular path always
equilateral triangle is √𝟑 times the area of it, keeping the rope streched and describes 88
then the length of each side of the triangle meters when it has traced out 720 at the
is. 𝟐𝟐
centre, the length of the rope is (𝑻𝒂𝒌𝒆 𝝅 = 𝟕 )
(a) 2 units (b) 3 units
(a) 7 m (b) 75 m
(c) 4 units (d) 6 units
(c) 82 m (d) 65 m

A
B
What is the area of a triangle having AB
perimeter 32 cm, one side 11 cm and
difference of other two sides 5 cm? A is the centre of circle whose radius is 8
(a) 𝟖√𝟑𝟎cm2 (b) 𝟓√𝟑𝟓cm2 and B is the centre of a circle whose
(c) 𝟔√𝟑𝟎cm 2
(d) 𝟖√𝟐 cm2 diameter is 8. If these two circles touch
externally, then the area of the circle with
4cm, 6cm 8cm diameter AB is.
(a) 36 𝝅 (b) 64 𝝅
(c) 144 𝝅 (d) 256 𝝅
Three circles of radius 4cm, 6 cm and 8 cm
touch each other pair wise externally. The
area of the triangle formed. By the line-
segments joining the centres of the three
circles is. The sides of a triangle having area 7776 sq.
(a) 144 √𝟏𝟑 sq. cm cm are in the ratio 3 : 4 : 5. The perimeter of
the triangle is:
(b) 12 √𝟏𝟎𝟓 sq. cm
(a) 400 cm (b) 412 cm
(c) 6 √𝟔 sq. cm (c) 424 cm (d) 432 cm
(d) 24 √𝟔 sq. cm

𝟔√𝟑 𝒄𝒎

If the length of each median of an equilateral

The cost of painting a room is Rs. 120. If the
triangle is 𝟔√𝟑 cm, the perimeter of the
width had been 4 meters less, the cost of the
triangle is.
Carpet would have been Rs. 20 less. The
(a) 24 cm (b) 32 cm
width of the room is.
(c) 36 cm (d) 42 cm
(a) 24 m (b) 20 m
(c) 25 m (d) 18.4 m
𝟏𝟐√𝟐 𝒄𝒎

A circle is inscribed in a square whose

length of the diagonal is 𝟏𝟐√𝟐 cm An
The floor of a corridor is 100 m long and 3 m
equilateral triangle is inscribed in that circle. wide. Cost of covering the floor with carpet
The length of the side of the triangle is. 50 cm wide at the rate of Rs. 15 per m is.
(a) 𝟒√𝟑 𝒄𝒎 (b) 𝟖√𝟑 𝒄𝒎 (a) Rs. 4500 (b) Rs. 9000
(c) 𝟔√𝟑 𝒄𝒎 (d) 𝟏𝟏√𝟑 𝒄𝒎 (c) Rs. 7500 (d) Rs. 1900
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A hall 25 meters long and 15 meters broad is The total area of a circle and a square is
surrounded by a varandah of uniform width equal to 5450 sq. cm. The diameter of the
of 3.5 meters. The cost of flooring the circle is 70 cm. What is the sum of the
varandah, at Rs. 27.50 per square meter is. circumference of the circle and the
(a) Rs. 9149.50 (b) Rs. 8146.50 perimeter of the square?
(c) Rs. 9047.50 (d) Rs. 4186.50 (a) 360 Cm (b) 380 Cm
(c) 270 Cm (d) None of these

The outer circumference of a circular race-

track is 528 metre. The track is everywhere The length of a rectangle is twice the
14 metre wide. Cost of levelling the track at diameter of a circle. The circumference of
the rate of Rs. 10 per sq. metre is. the circle is equal to the area of a square of
(a) Rs. 77660 (b) Rs. 67760 side 22 cm. What is the breadth of the
(c) Rs. 66760 (d) Rs. 76760 rectangle if its perimeter is 668 cm?
(a) 24 cm (b) 26 cm
(c) 52 cm (d) None of these

The cost of fencing a circular plot at the rate

of Rs. 15 per meter is Rs. 3300. What will be
the cost flooring the plot at the rate of Rs.
100 per square metre? The length of a rectangle is three fifth of the
(a) Rs. 3,85,000 side of a square. The radius of a circle is
(b) Rs. 2,20,000 equal to side of the square. The
(c) Rs. 3,50,000 circumference of the circle is 132 cm. What
(d) Cannot be determined is the area of the rectangle if the breadth of
(e) None of these the rectangle is 8 cm?
(a) 112.4 sq. cm (b) 104.2 sq. cm
(c) 100.8 sq. cm (d) None of these

= 𝟏𝟒
𝑫𝑪 = 𝑪𝑬, ∆BDE
If the diameter of each circle is 14 cm and DC
The perimeter of a square is equal to twice = CE, the area of ∆BDE is
the perimeter of a rectangle of length of 8
cms and breadth 7 cms. What is the
circumference of a semicircle whose
diameter is equal to the side of the square?
(Rounded off to the two decimal places)
(a) 38.57 cms.
(b) 23.57 cms.
(c) 42.46 cms. (a) 784 sq. cm. (b) 748 sq. cm.
(d) 47.47 cms. (c) 874 sq. cm. (d) 441 sq. cm.

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ABCD
The area of the shaded region of square
ABCD is
The perimeter of a rhombus is 40 cm, If one
of the diagonals be 12 cm long, what is the
length of the other diagonal?
(a) 12 cm (b) √𝟏𝟑𝟔cm
(c) 16 cm (d) √𝟒𝟒 cm

(a) 186 sq. cm. (b) 168 sq. cm

(c) 188 sq. cm. (d) 198 sq. cm.

A parallelogram has sides 15 cm and 7 cm

long. The length of one of the diagonals is 20
cm. The area of the parallelogram is.
(a) 42 cm2 (b) 60 cm2
2
The area of a rectangular park is 1050 sq.m (c) 84 cm (d) 96cm2
and its perimeter is 130 metre. There is 2.5 m
wide path inside the park all around. The
cost of construction of path is Rs. 40 per sq.
metre. Find the total cost of construction of
whole path.
(a) Rs. 10000 (b) Rs. 12000
The lengths of two parallel sides of a
(c) Rs. 12500 (d) Rs. 8500
trapezium are 6 cm and 8 cm. If the height of
the trapezium be 4 cm, then its area is.
(a) 28 cm2 (b) 56 cm2
2
(c) 30 cm (d) 36 cm2

A cube whose length is 25 cm. How many

cubes with sides 5 cm can be made by
The length and breadth of the floor of a room melting it?
are 20 feet and 10 feet respectively. Square (a) 125 (b) 225
tiles of 2 feet length of three different (c) 200 (d) 175
colours are to be laid on the floor. Black tiles
are laid in the first row on all sides. If white
titles are laid in the one-third of the
remaining and blue tiles in the rest. how
many blue tiles will be there? 3 cubes of iron whose sides are 6 cm, 8 cm
(a) 16 (b) 32 and 10 cm respectively. Find the side of the
(c) 48 (d) 64 cube formed by melting these 3 cubes?
(a) 14 (b) 15
(c) 12 (d) 20

The diagonals of a rhombus are 32 cm and

24 cm respectively. The perimeter of the
rhombus is:
(a) 80 cm (b) 72 cm A cuboid has been formed by adding 2
(c) 68 cm (d) 64 cm cubes with sides 8 cm. find the area of the
entire surface of that cuboid?
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(a) 320 (b) 640 (a) 2 (b) 20

(c) 800 (d) 1200 (c) 200 (d) 2000

How many boxes of 8 cm long 7 cm wide and

6 cm high can be placed in a room 8 m long
7 m wide 6 m high.? A pond whose length is 24 m and width is 15
(a) 1000000 (b) 8000000 m. Some people take a dip in this pond,
(c) 100000 (d) 1500000 which increases the water level by 1 cm.
Each person replaces 0.1 m3 of water, then
how many people descend into the pond?
(a) 30 (b) 24
(c) 35 (d) 36

How many bricks are needed to make an 8 m √𝟏𝟐

long 6 m high and 22.5 cm wide wall, while
each brick is 25 cm long by 11.25 cm. Wide If diagonal of a cube is √𝟏𝟐 cm then its
and 6 cm are high? volume is cm3 is
(a) 6400 (b) 3200 (a) 8 (b) 12
(c) 7500 (d) 5000 (c) 24
𝟑
(d) √𝟐

𝟏
𝟑

What is the maximum length a box can be 𝟏 𝟏

placed in a 12m long 9m wide and 8m high 𝟑 𝟐
room? A cuboidal water tank has 216 litres of water.
(a) 17 (b) 20 𝟏 𝟏
Its depth is of its length and breadth is of
(c) 25 (d) 25 𝟑 𝟐
𝟏
𝟑
of the difference of length and breadth. The
length of the tank is.
(a) 72 dm (b) 18 dm
(c) 6 dm (d) 2 dm


A rectangular vessel whose length is 20 cm 
and width is 15 cm is filled with water. If a
cube with a side of 15 cm is immersed in it,
then what will be the increase in the water A wooden box measures 20 cm by 12 cm by
level? 10 cm. Thickness of wood is 1 cm. Volume
(a) 22.5 (b) 11.25 of wood to make the box (in cubic cm) is
(c) 11.5 (d) 25 (a) 960 (b) 519
(c) 2400 (d) 1120

There is 42000 litters of water in a

rectangular pond. If the length of reservoir /
pond is 6 m and width is 3.5 m, then give the
depth of reservoir / pond. ?

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A rectangular sheet of metal is 40 cm by 15 The length of the largest possible rod that
cm. equal squares of side 4 cm are cut off at can be placed is a cubical room is
the corners and the remaining is folded up 𝟑𝟓√𝟑m.The suface area of the largest
to form an open rectangular box The volume possible sphere that fit within the cubical
of the box is. 𝟐𝟐
room (assuming 𝝅 = 𝟕 ) (in sq. m) is
(a) 896 cm3 (b) 986 cm3
(c) 600 cm 3
(d) 916 cm3 (a) 3,500 (b) 3,850
(c) 2,450 (d) 4,250
x

The floor of a room is of size 4 m x 3 m and

its height is 3 m. The walls and ceiling of the Three solid iron cubes of edges 4 cm, 5 cm
room require painting. The area to be and 6 cm are melted together to make a new
painted is. cube. 62 cm3 of the melted material is lost
(a) 66 m2 (b) 54 m2 due to improper handling. The area (in cm2)
(c) 42 m2 (d) 33 m2 of the whole surface of the newly formed
cube is.
(a) 294 (b) 343
(c) 125 (d) 216

The area of the four walls of a room is 660 m2

and its length is twice its breadth. if the
height of the room is 11m, then area of its
floor (in m2) is.
(a) 120 (b) 150
(c) 200 (d) 330 A low land, 48m long and 31.5 m broad is
raised to 6.5 dm. For this, earth is removed
from a cuboidal hole, 27 m long and 18.2 m
broad, dug by the side of the land. The depth
of the hole will be.
(a) 3 m (b) 2 m
A Cuboid whose sides are in ratio 2 : 4 : 8
(c) 2.2 m (d) 2.5 m
have the same volume as a cube. The ratio
of their surface area is:
(a) 7 : 5 (b) 4 : 3
(c) 8 : 5 (d) 7 : 6

(in cm)
If the sum of the length, Breadth and height A rectangular field with a length of 40 m and
of a rectangular paralleopiped is 24 cm and width of 28 m, a 12 m long 6 m wide and 5 m
the length of its diagonal is 15 cm, then its deep pit was dug on one corner and the soil
total surface area is. extracted from it was spread evenly in the
(a) 256 cm2 (b) 265 cm2 remaining part of the field. How high will the
(c) 315 cm2 (d) 351 cm2 level rise? (in cm)
(a) .3425 (b) 34.25
(c) 342.5 (d) 3.425
𝟑𝟓√𝟑 𝒎𝒕𝒓.

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The ratio of the radius of two cylinders is 2: (c) 40 cm (d) 50 cm

3 and the ratio of their height is 5: 3, then find
the ratio of their volume?
(a) 20 : 27 (b) 27 : 25
(c) 27:20 (d) 25 : 23

Coins of 0.75 cm radius and 0.2 cm

thickness melt 3 cm. How many coins will be
required to make a cylinder of radius 3cm
The ratio of the diameters of two equal and 8 cm height?
volume cylinders is 3: 2. Find the ratio of (a) 840 (b) 640
their height? (c) 1000 (d) 720
(a) 4 : 9 (b) 2 : 5
(c) 9 : 4 (d) 5 : 2

What part of a 48 m long 16.5 m wide and 4

The ratio of the radius and height of a cone m deep trench can be filled with soil
is 4: 3. Find the ratio of the area of its curved obtained by digging a 56 m long cylindrical
surface and the entire surface? tunnel with a diameter of 4 m?
(a) 9 : 5 (b) 5 : 9 (a) 11.11% (b) 22.22 %
(c) 7 : 2 (d) 5 : 3 (c) 33.33% (d) 44.44%

Find the radius of that big sphere formed by A conical tent can accommodate up to 22
melting three spheres whose radius are 3 people. Each person occupies a space of 4
cm, 4 cm and 5 cm respectively? m2 and each person needs 40 m3 of air to
(a) 5 (b) 6 breathe. Find the height of the cone?
(c) 7 (d) 8 (a) 22 (b) 35
(c) 28 (d) 30

Find the length of the wire converted by

beating a copper sphere of radius 3 cm into The radius of the base of a conical tent is 7
a wire of diameter 0.2 cm? m and height is 24m. To make it 1.25m wide
(a) 36 m (b) 45 m and how long cloth will be required?
(c) 40 m (d) 50 m (a) 440 (b) 300
(c) 600 (d) 640

The radius of a cylindrical vessel is 18 cm 22 cm long and 12 cm wide. A rectangular

and height is 32 cm which is filled with sand. sheet is made by turning its length
It was made a cone from sand by reversing perpendicular to a cylinder and tell the
it on earth. If the height of the cone is 24 cm, volume of the cylinder?
find the radius? (a) 360 (b) 462
(a) 36 cm (b) 45 cm
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(c) 562 (d) 160

The volume of a right circular cylinder is

equal to the volume of that right circular
22 m long and 20 m wide water falls from a cone whose height is 108 cm and diameter
rectangular roof into a cylindrical vessel of base is 30 cm. If the height of the cylinder
whose diameter is 2 m and height is 3.5 m. If is 9 cm, the diameter of its base is
the container is full then how much rain (in (a) 30 cm (b) 60 cm
cm)? (c) 50 cm (d) 40 cm
(a) 3 (b) 4.5
(c) 3.5 (d) 2.5

A hollow cylindrical tube 20 cm long is made

or iron and its external and internal
A sphere of radius 2 cm is immersed in a diameters are 8 cm and 6 cm respectively.
cylinder filled with water whose radius is 4 The volume of iron used in making the tube
cm. If the sphere is completely submerged 𝟐𝟐
is (𝝅 = 𝟕 )
in water, how much will the water level rise
in the cylinder? (a) 1760 cm2 (b) 880 cm3
(a) 0.11 (b) 0.22 (c) 440 cm3 (d) 220 cm3
(c) 0.66 (d) 0.44

A well 20 m in diameter is dug 14 m deep and

From a pipe of 14 cm diameter, waterfalls at the earth taken out is spread all around it to
a width of 5 m to form an embankment. The
a speed of 5 km / hour in a 50 m long and 44
m wide tank, how many hours will it take to height of the embankment is:
lift the surface of water 7 cm high? (a) 10m (b) 11m
(a) 2 (b) 4 (c) 11.2m (d) 11.5m
(c) 3 (d) 5

In a right circular cone, the radius of its base

The height of a conical tank is 60 cm and the is 7 cm and its height 24 cm. A cross- section
diameter of its base is 64 cm. The cost of is made through the midpoint of the height
painting it from outside at the rate of Rs. 35 parallel to the base. The volume of the upper
portion is
per sq. m. is:
(a) Rs. 52.00 approx (a) 169 cm3 (b) 154 cm3
3
(b) Rs. 39.20 approx (c) 1078 cm (d) 800 cm3
(c) Rs. 35.20 approx
(d) Rs. 23.94 approx

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𝟏 (c) 40,000 m3 (d) 4,000 m3
𝟐𝟕

The height of the cone is 30 cm. A small cone

is cut off at the top by a plane parallel to its
𝟏
base. If its volume is 𝟐𝟕 of the volume of the
cone. At what height above the base, is the
Water is flowing at the rate of 3 km/hr
section made?
through a circular pipe of 20 cm internal
(a) 6 cm (b) 8 cm
diameter into a circular cistern of diameter
(c) 10 cm (d) 20 cm
10 m and depth 2 m. In how much time will
the cistern be filled?
(a) 1 hour
(b) 1 hour 40 minutes
(approx) (c) 1 hour 20 minutes
A semi-circular sheet of metal of diameter 28 (d) 2 hour 40 minutes
cm is bent into an open conical cup. The
depth of the cup is approximately.
(a) 11 cm (b) 12 cm
(c) 13 cm (d) 14 cm

The diameter of a 120 cm long roller is 84 cm.

It takes 500 complete revolutions of the
roller to level a ground. The cost of levelling
the ground at Rs. 1.50 sq. m. is:
A solid wooden toy is in the shape of a right (a) Rs. 5750 (b) Rs. 6000
circular cone mounted on a hemisphere. If (c) Rs. 3760 (d) Rs. 2376
the radius of the hemisphere is 4.2 cm and
the total height of the toy is 10.2 cm. Find the
volume of wooden toy (nearly)?
(a) 104 cm3 (b) 162 cm3
3
(c) 421 cm (d) 266 cm3
The diameter of two hollow spheres made
from the same metal sheet are 21 cm and
17.5 cm respectively. The ratio of the area of
metal sheets required for making the two
spheres is
(a) 6:5 (b) 36:25
Assume that a drop of water is spherical and (c) 3:2 (d) 18:25
its diameter is one-tenth of a cm. A conical
glass has a height equal to the diameter of
its rim. If 32,000 drops of water fill the glass
completely. Then the height of the glass (in
cm) is A cone, a hemisphere and a cylinder stand
(a) 1 (b) 2 on equal bases and have the same height.
(c) 3 (d) 4 The ratio of their respective volume is
(a) 1:2:3 (b) 2:1:3
m m (c) 1:3:2 (d) 3:1:2

A river 3 m deep and 40 m wide is flowing at

the rate of 2 km per hour, How much water The diameter of the moon is assumed to be
(in-litres) will fall into sea in a minute? one fourth of the diameter of the earth. Then
(a) 4,00,000 m3 (b) 40,00,000 m3
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the ratio of the volume of the earth to that of

the moon is
(a) 64:1 (b) 1:64
(c) 60:7 (d) 7:60

x x
𝝅 = 𝟐𝟐/𝟕
Four circles of equal radius are described
𝟐𝟐 about the four corners of a square so that
𝝅= each touches two of the other circles. If each
𝟕
side of the square is 140 cm then area of the
A cone of height 7 cm and base radius 1 cm space enclosed between the circumference
is carved from a cuboidal block of wood 10 of the circle is (take 𝝅 = 𝟐𝟐/𝟕)
𝟐𝟐
cm x 5 cm x 2 cm. [Assuming = 𝟕 ] The (a) 4200 cm2 (b) 2100 cm2
2
(c) 7000 cm (d) 2800 cm2
percentage wood wasted in the process is:
𝟐 𝟏
(a) 𝟗𝟐 % (b) 𝟒𝟔 %
𝟑 𝟑
𝟏 𝟏
(c) 𝟒𝟐 𝟑% (d) 41𝟑%

A hemispherical bowl of internal radius 9

cm, contains a liquid. This liquid is to be
filled into small cylindrical bottles of
diameter 3 cm and height 4 cm. Then the
number of bottles necessary to empty the
The shape of an object is a right circular bowl is.
cylinder with a hemisphere on bottom and a (a) 18 (b) 45
right circular cone on the top. The radius of (c) 27 (d) 54
the cylindrical part is 5 cm and the height of
cylinder part is 2.6 times the radius. What is
the total height of the object, if the surface
area of the object is 770 cm2?
(a) 18 cm (b) 35 cm
(c) 12 cm (d) 30 cm

A right circular cylinder having diameter 21

𝟏 cm & height 38 cm is full of ice cream. The
𝟐 ice cream is to be filled in cones of height 12
cm and diameter 7 cm having a
% hemispherical shape on the top. The number
of such cones to be filled with ice cream is
An inverted conical shaped vessel is filled (a) 54 (b) 36
with water to its brim. The height of the (c) 44 (d) 24
vessel is 8 cm and radius of the open end is
5 cm. When a few solid spherical metallic
𝟏
ball each of radius 𝟐 cm are dropped in the
vessel, 25% water is overflowed. The A
number of balls is: B
(a) 100 (b) 400 A B
(c) 200 (d) 150
The four walls and celling of a room of length
25 m, breadth 12 m and height 10 m are to be
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painted. Painter A can paint 200 m2 in 5 days,

painter B can paint 250 m2 in 2 days. If A and
B work together, they will finish the job in. The cross section of a canal is in the shape
𝟏𝟎
(a) 6 days (b) 𝟔 𝟑𝟑 days of an isosceles trapezium which is 2 m wide
(c) 𝟕
𝟏𝟎
days (d) 8 days at the bottom and 3 m wide at the top. If the
𝟑𝟑 depth of the canal is 1 m and it is 100 m long,
what is the maximum capacity of this canal?
(a) 500 cubic mts (b) 250 cubic mts
(c) 750 cubic mts (d) 1000 cubic mts

cm, cm cm,
cm
The external and the internal radius of a
hollow right circular cylinder of height 15 cm The base of a solid right prism is a triangle
are 6.75 cm and 5.25 cm respectively. If it is whose sides are 9 cm, 12 cm and 15 cm. The
melted to form a solid cylinder of height half height of the prism is 5 cm. Then the total
of the original cylinder, then the radius of the surface area of the prism is
solid cylinder is (a) 180 cm2 (b) 234 cm2
(a) 6 cm (b) 6.5 cm (c) 288 cm 2
(d) 270cm2
(c) 7 cm (d) 7.25 cm

The base of a right prism is a trapezium. The

length of the parallel sides are 8 cm and 14
cm and the distance between the parallel
A right circular cylinder is partially filled with sides is 8 cm, If the volume of the prism is
water. Two iron spherical balls are 1056 cm3, then the height of the prism is
completely immersed in the water so that the (a) 44 cm (b) 16.5 cm
height of the water in the cylinder rises by 4 (c) 12 cm (d) 10.56 cm
cm. If the radius of one ball is half of the
other and the diameter of the cylinder is 18
cm, then the radii of the spherical balls are
(a) 6 cm and 12 cm (b) 4 cm and 8 cm
(c) 3 cm and 6 cm (d) 2 cm and 4 cm
The Perimeter of the triangular base of a
right prism is 15 cm and radius of the incircle
of the triangular base is 3 cm. If the volume
of the prism be 270 cm3 then the height of
the prism is
Parallel sides of a trapezium are 14 cm and (a) 6 cm (b) 7.5 cm
35 cm and the area is 1176 cm2. What is the (c) 10 cm (d) 12 cm
value of the distance (in cm) between
parallel sides?
(a) 72 (b) 96 cm2
(c) 24 (d) 48 cm3

The base of a right prism is an equilateral

triangle of area 173 cm2 and the volume of

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the prism is 10380 cm3. The area of the

lateral surface of the prism is (use √𝟑 = 1.73)
(a) 1200 cm2 (b) 2400 cm2
2
(c) 3600 cm (d) 4380 cm2

Height of a prism – shaped part of a machine

cm is 8 cm and its base is an isosceles triangle,
cm2 whose each of the equal sides is 5 cm and
The height of a right prism with a square remaining side is 6 cm. The volume of the
base is 15 cm. If the area of the total surface part is
of the prism is 608 sq. cm, its volume is (a) 90 cm3 (b) 96 cm3
(a) 910 cm3 (b) 920 cm3 (c) 120 cm 3
(d) 86 cm3
3
(c) 960 cm (d) 980 cm3

𝟑√𝟑
( ) P2
cm cm 𝟐
cm cm2, 100√𝟑 cm cm3 P
3
gm/cm
A prism has base a right angled triangle If the area of the base, height and volume of
whose sides abjacent to the right angles are 𝟑√𝟑
a right prism be ( 𝟐 ) P2 cm2, 100 √𝟑 cm and
10 cm and 12 cm long. The height of the
7200 cm3 respectively, then the value of P (in
prism is 20 cm. the density of the material of
cm) will be?
the prism is 6gm/cubic cm. the weight of the 𝟐
prism is (a) 4 (b)
√𝟑
(a) 6.4 kg (b) 7.2 kg 𝟑
(c) √𝟑 (d) 𝟐
(c) 3.4 kg (d) 4.8 kg

ABCD
AB = 9 BC = 14 CD = 13
0
DA = 12 ∠DAB = 90
If the radius of the circular ends of a frustum
which is 45 cm high be 28 cm and 7 cm then
the capacity of the bucket in cubic
The base of a right prism is a quadrilateral centimetre is?
ABCD, given that AB = 9 cm, BC = 14 cm, CD (a) 48510 (b) 45810
= 13 cm, DA = 12 cm and ∠DAB = 900. If the (c) 458150 (d) 48051
volume of the prism be 2070 cm3, then the
area of the lateral surface is
(a) 720 cm2 (b) 810 cm2
(c) 1260 cm2 (d) 2070 cm2
𝟐𝟐
(𝝅 = )
𝟕
The radius of two circular faces of the
frustum of a cone of height 21cm and 3cm
and 2cm respectively. What is the volume of
𝟐𝟐
the frustum of the cone is cm3 (𝝅 = 𝟕 )?
Base of a right prism is a rectangle, the ratio (a) 154 (b) 286
of whose length and breadth is 3 : 2. If the (c) 345 (d) 418
height of the prism is 12 cm and total surface
area is 288 sq. cm, the volume of the prism
is:
(a) 288 cm3 (b) 290 cm3
3
(c) 286 cm (d) 291 cm3

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A cone of radius 4 cm with a slant height of

12 cm was sliced horizontally resulting into The base of a right pyramid is a square of
a smaller cone (upper portion) and a frustum side 40 cm long. If the volume of the pyramid
(lower portion). If the ratio of the curved is 8000 cm3, then its height is :
Surface area of the upper smaller cone and (a) 5 cm (b) 10 cm
the lower frustum is 1 : 2. What will be the (c) 15 cm (d) 20 cm
slant height of the frustum?
(a) 12 – √𝟑 (b) 12 – 2√𝟑
(c) 12 – 3√𝟑 (d) 12 – 4√𝟑

The base of a right pyramid is a square of

side 16 cm long. If its height be 15 cm, then
the area of the lateral surface in square cm
is:
(a) 136 (b) 544
(c) 8000 (d) 1280
The radius of top and bottom of frustum is 3
cm and 6 cm respectively. Its height is 8 cm.
There is a conical cavity of height 3 cm and
radius 6 cm at the bottom. The amount of Area of the base of a pyramid is 57 sq. cm.
material in the solid is? and height is 10 cm, then its volume (in cm3),
(a) 168 𝝅 (b) 132 𝝅 is
(c) 36 𝝅 (d) 204 𝝅 (a) 570 (b) 390
(c) 190 (d) 590

If the base of a right pyramid is triangle of

sides 5 cm, 12 cm and 13 cm and its volume
The height of right circular cone & radius of is 330 cm3, then its height (in cm) will be
its circular base are 9 cm and 3 cm (a) 33 (b) 32
respectively. The cone is cut by a plane (c) 11 (d) 22
parallel to its base so as to divide into tow
parts. The volume of the frustum is 44 cm3.
𝟏𝟎 √𝟑
Find the radius of the upper surface of
sructum?
𝟑
(a) √𝟏𝟐 cm
𝟑
(b) √𝟏𝟑 cm √𝟑
𝟑 𝟑
(c) √𝟔 cm (d) √𝟐𝟎 cm
The base of a right pyramid is equilateral
triangle of side 10√𝟑 cm. If the total surface
area of the pyramid is 270√𝟑 cm2. Its height
is
𝝅
(a) 12√𝟑 cm (b) 10 cm
The lateral surface area of frustum of a right (c) 10√𝟑 cm (d) 12 cm
circular cone if the area of its base is 16𝝅
cm2 and the diameter of circular upper
surface is 4 cm and slant height 6 cm, will
be?
(a) 30 𝝅 cm2 (b) 48 𝝅 cm2
2
(c) 36 𝝅 cm (d) 60 𝝅 cm2
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Base of a pyramid is in form of regular ABCD BEFG

Hexagon which side is 20 cm long. If the
heights of the pyramid is 10 cm. Find its
lateral surface area
In the given figure, ABCD and BEFG are
(a) 1000 (b) 1200
squares of sides 8 cm and 6 cm respectively.
(c) 800 (d) 1500
What is the area (in cm2) of the shaded
region?

(a) 12 (b) 14
A metallic hemispherical bowl is made up of (c) 10 (d) 16
steel. The total steel used in making the bowl
is 342𝝅 cm3. The bowl can hold 144𝝅 cm3 ABCD P, AB
water. What is the thickness (in cm) of bowl
and the curved surface area (in cm2) of outer DP = 13, CP = 10 BP = 6 AP
side?
(a) 6,162𝝅 (b) 3,162 𝝅
(c) 6, 81 𝝅 (d) 3,81 𝝅 ABCD is a rectangle. P is a point on the side
AB as shown in the given figure. If DP = 13,
CP = 10 and BP = 6, then what is the value of
AP?
D C

A P B
(a) √𝟏𝟎𝟓 (b) √𝟏𝟑𝟑
A hollow cylinder is made up of metal. The (c) 12 (d) 10
difference between outer and inner curved
surface area of this cylinder is 352 cm2.
Height of the cylinder is 28 cm. If the total
surface area of this hollow cylinder is 2640
cm2, then what are the inner and outer radius A solid cube is cut into 27 identical cubes.
(in cm)? What is the percentage increase in the total
(a) 4, 6 (b) 10, 12 surface area?
(c) 8, 10 (d) 6, 8 (a) 150 (b) 200
(c) 300 (d) 250
ABCDEF

XA = 7
In the given figure, ABCDEF is a regular
hexagon whose side is 12 cm. What is the
shaded area (in cm2)? In the given figure, four identical semicircles
and drawn in a quadrant. XA = 7 cm. What is
the area (in cm2) of shaded region?

(a) 54√𝟑 (b) 36√𝟑

(c) 48√𝟑 (d) 52√𝟑
(a) 70 (b) 140 (c) 77 (d) 84
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ABC
AB = 21 BC=
28 AC = 35
In the given figure, two squares of sides 8
cm and 20 cm are given. What is the area (in In the given figure, 3 semicircles are drawn
cm2) of the shaded part? on three sides of triangle ABC. AB = 21 cm,
BC = 28 cm and AC = 35 cm. What is the area
(in cm2) of the shaded part?

𝟏𝟐𝟎 𝟏𝟔𝟎
(a) (b)
𝟕 𝟕 (a) 588 (b) 324
𝟏𝟖𝟎 𝟐𝟒𝟎
(c) (d) (c) 294 (d) 286
𝟕 𝟏𝟑

ABCD ABCD

EFGH EFGH
LMNO
LMNO
The ratio of curved surface area of a right
circular cylinder to the total area of two ABCD
bases is 2 : 1. If the total surface area of the
cylinder is 23100 cm2, then what is the In the given figure, ABCD is a square. EFGH
volume (in cm3) of cylinder? is a square formed by joining mid points of
(a) 247200 (b) 269500 sides of ABCD. LMNO is a square formed by
(c) 312500 (d) 341800 joining mid points of sides of EFGH. A circle
is inscribed inside LMNO. If area of circle is
ABCD 38.5 cm2, then what is the area (in cm2) of
E F AB DC square ABCD?
EPF,
EF LMNO

In the given figure, ABCD is a square of side

14 cm. E and F are mid points of sides AB
and DC respectively. EPF is a semicircle
whose diameter is EF. LMNO is a square.
What is the area (in cm2) of the shaded
region?
(a) 98 (b) 196
(c) 122.4 (d) 171.5

(a) 108.5 (b) 94.5

(c) 70 (d) 120

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