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MENSURATION
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MENSURATION
Level - 1
Q1. If the radius and heights of two cylinders are in the ratio of 5: 6 and 2: 5
respectively, then find the ratio of volume of two cylinders?
(a) 6:17
(b) (b)8:15
(c) 5:18
(d) 7:19
(e) None of these

ANSWER: C

Q2. If the radius and heights of the two cylinders arc 5: 6 and 5: 8, then whatis
the ratio of its volume?
(a) 108:193
(b) 95:178
(c) 125:288
(d) 112:257
(e) None of these

ANSWER: C

Q3. The perimeter of a rectangular field is twice the perimeter of a squarefield.

If one of the sides of the square field is 20 m and breadth of the rectangular
field is 30m then find the area of the rectangular field?
(a) 1250 sq m
(b) 1300 sq m
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(c) 1350 sq m
(d) 1500 sq m
(e) None of these

ANSWER: D

Q4. Find the respective ratio of the volumes of a sphere and a cylinder, both
having radius 14cm and the height of the cylinder is l6 cm?
(a) 5:8
(b) 7:6
(c) 6:7
(d) 8:5
(e) None of these

ANSWER: B

Q5. The ratio of length and breadth of the rectangular park is 3: 2. If the man
cycling along the boundary of the park at the speed of 12 km/hr completes one
round in 10 minutes, then find the area of the park?
(a) 160000 sq. m
(b) 280000 sq. m
(c) 220000 sq. m
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(d) 240000 sq. m

(e) None of these

ANSWER: D

Q6.Calculate the ratio of curved surface area and total surface area of a cone
whose diameter is 4Om and height is 21m?
(a) 21:32
(b) 24:49
(c) 25:52
(d) 18:35
(e) None of these

ANSWER: B

Q7. There are two circles of different radii. The area of a square is 196 sq cm,
whose side is half the radius of the larger circle. The radius of the smaller circle
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is three sevenths that of the larger circle. What is the circumference of the
smaller circle?
(a) 32 π cm
(b) 12 π cm
(c) 16 π cm
(d) 24 π cm
(e) 18 π cm

ANSWER: D

Q8. The ratio of the angles of a quadrilateral is 3:4:6:7. Half the second largest
angle of the quadric lateral is equal to the smaller angle of a parallelogram.
What is the value of the adjacent angle of the parallelogram?
(a) 126˚
(b) 94˚
(c) 196˚
(d) 96˚
(e) None of these
ANSWER: A
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Q9. If the radius and heights of the two cylinders are 4:7 and 3: 8, then whatis
the ratio of its volume?
(a) 14:9
(b) 6:49
(c) 9:1
(d) 6:7
(e) None of these

ANSWER: B

Q10. Water flows into an empty tank of dimensions 3.5 m * 4.4 m through a pipe
of cross-sectional radius 7 cm at 10 kmph. In how many minutes will thelevel of
water in the tank reach three metres?
(a) 30 min
(b) 24 min
(c) 18 min
(d) 12 min
(e) None of these“

ANSWER: C

Q11. There is a circular plot of radius 21 metres. A Circular seating space is

constructed at the centre of the plot at a total cost of Rs. 231 at Rs. 6 per square
metre. What is the area of the remaining part of the circular plot?
(a) 1245 sq m
(b) 1574.25 sq m
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(c) 1506.75 sq m
(d) 1347.5 sq m
(e) 1386 sq m
ANSWER: D

Q12. The diameter of a smaller circle and a larger circle are the side of a square
and the diagonal of the square respectively. If the side of the square is4cm,
what is the ratio of the areas of the smaller circle and the larger circle?
(a) 2:1
(b) 1:2
(c) 1:√2
(d) √2:1
(e) None of these

ANSWER: B

Q13. The ratio of the angles of a quadrilateral is 3: 4:6:7. Half the second biggest
angle of the quadrilateral is equal to the smaller angle of a parallelogram. What
is the value of the adjacent angle of the parallelogram?
(a) 96˚
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(b) 94˚
(c) 126˚
(d) 136˚
(e) None of these

ANSWER: C

Q14. The volume of a cylindrical tank is 1584 m3. Its radius and height are inthe
ratio of 3:7. What is the height of the tank?
(a) 12 m
(b) 15 m
(c) 21 m
(d) 14 m
(e) None of these

ANSWER: D

Q15. A rectangular solid metal which is 36 cm long 18 cm broad and 3 cm high

is to be melted and cast into two different cubes, the volume of the biggerbeing
eight times that of the smaller one .Find the surface area of the smaller cube?
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(a) 180 cm^2

(b) 36 cm^2
(c) 144 cm^2
(d) 150 cm^2
(e) None of these

ANSWER: E

Q16.Find the respective ratio of the volumes of a sphere and a cylinder both
having radius 14cm and the height or the cylinder is l6 cm?
(a) 5:8
(b) 7:6
(c) 6:7
(d) 8:5
(e) None of these

ANSWER: B

Q17. The radius of the circle is equal to two-third of the side of the square.The
area of the square is 441 sq cm. Find the perimeter of a circle?
(a) 66 cm
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(b) 77 cm
(c) 88 cm
(d) 121 cm
(e) None of these
ANSWER: C

Q18. The area of a square is 1024 sq cm. What is respective ratio between the length
and the breadth of a rectangle whose length is twice the side of square and
breadth is 12 cm less than the side of square?
(a) 5:16
(b) 16:5
(c) 14:5
(d) 32:5
(e) None of these
ANSWER: B

Q19. The length and breadth of a rectangular piece of land arc in the ratio of 5:
3. The owner spent Rs 3000 for surrounding it from all the sides at the rateof Rs
7.50 per meter. The difference between length and breadth is?
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(a) 50 m
(b) 100 m
(c) 200 m
(d) 150 m
(e) None of these

ANSWER: A

Q20. The radius of the semicircle is equal to the half the side of the square. The
area of the square is 1024 Sq. Cm. Find the perimeter of the Semicircle?
(a) 32π
(b) 24 π
(c) 16 π+32
(d) 28 π
(e) None of these
ANSWER: C

Q21. The length of a rectangle is 4m more than the side of the square and the
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breadth of the rectangle is 4m less than the side of the square it the area of the
square is 576 sq m. what is the area of the rectangle?
(a) 680
(b) 264
(c) 456
(d) 560
(e) None of these

ANSWER: D

Q22. The angles of quadrilateral are in the ratio of 2:4:5:7. The highest angleof
quadrilateral is half of the smallest angle of parallelogram. Find the adjacent
angle of parallelogram?
(a) 120˚
(b) 90˚
(c) 80˚
(d) 110˚
(e) None of these
ANSWER: D

Q23.The difference between simple interest and compound interest on Rs.28750

at the rate of 8% per annum for 2 years is?
(a) Rs.158
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(b) Rs.184
(c) Rs.176
(d) Rs.162
(e) None of
these

ANSWER: B

Q24. A 4m wide road is running around a angular field of length 28m and
breadth 24m. Find the difference between the area of the rectangular field and
the area of the road?
(a) 140cm2
(b) 192cm2
(c) 170cm2
(d) 162cm2
(e) None of these

ANSWER: B

Q25. A cylindrical roller rolls over a square filed. It takes 700 rounds to coverthe
complete field. If the radius of the cylindrical roller is O.81 meter and length is
16m then find out the side of square (approximately).
(a) 325m
(b) 239m
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(c) 319m
(d) 378m
(e) 250m

ANSWER: B

Q26. Two cubes have their volumes in the ratio 8:27. Find the ratio of their
surfaces?
(a) 4:5
(b) 4:9
(c) 8:3
(d) 6:2
(e) 8:5

ANSWER: B

Q27.If the base of the prism is in form of an equilateral triangle of side 8cmand
its volume is 64√3 cm3.Then the height of prism in cm?
(a) 6cm
(b) 4cm
(c) 5cm
(d) 8cm
(e) 9cm
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ANSWER: B

Q28. A road of width 8m is running around a square field of side 42m from outside.
Find the difference between area of the square field and the area of the road?
(a) 132 m2
(b) 164 m2
(c) 152 m2
(d) 184m2
(e) None of these

ANSWER: B

Q29. The diameter of the base of a cylindrical drum is 98 cm and its height is 21
cm. It is full of water. How many tins, each of length 21 cm breadth 11 cm and
height 2 cm can be filled with water from the drum?
(a) 563
(b) 452
(c) 343
(d) 288
(e) None of these

ANSWER: C
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Q30. The length of a rectangle is 4/7 of the side of a square. The radius of a circle
is equal to the Side of the square. The Circumference of the circle is 396cm and
the breadth of the rectangle is 6cm. W hat is area of the rectangle?
(a) 276cm2
(b) 310cm2
(c) 216cm2
(d) 256cm2
(e) None of these

ANSWER: C

Q31. The area of the square is 1296 square meters. The breadth of the
rectangle is 1/3 of the side of the square and the length of the rectangle is
twice the breadth What is the difference between the area of the square and
area of the rectangle?
(a) 1120m2
(b) 1055m2
(c) 1008m2
(d) 1111m2
(e) None of these

ANSWER: C

Q32. A square botanical garden is having a side of 28m. The gardener alreadyleft
2m wide outside the garden along its side. Gardener plans to construct a path by
using tiles having (12*10) cm dimension. Each tile costs Rs.5 (including
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construction cost). Find overall expenditure needed for completion?

(a) 150000
(b) 200000
(c) 100000
(d) 225000
(e) None of these

ANSWER: C

Q33.If the difference between length and breadth of a rectangle is 5m and

perimeter of the rectangle is 350m. Find the circumference of larger circle thatyou
can draw inside thee rectangle?
(a) 217.14m
(b) 232.25m
(c) 244.14m
(d) 267.14m
(e) None of these

ANSWER: D

Q34. A wire is looped in the form of circle of diameter 56 cm. It is rebent in the
shape of a square. Find the length of the diagonal of the largest square that can
be formed?
(a) 44√2
(b) 88√2
(c) 22√2
(d) 44
(e) 88
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ANSWER: A

Q35. If A rectangular sheet of metal is 80 cm by 35cm. Equal squares of side 3cm

are cut off at the comers and the remainder is folded up to form an open
rectangular box. Then that ox is converted into same rectangle box which in
12*21 cm. Find the No of box that we can get as maximum?
(a) 59
(b) 65
(c) 70
(d) 63
(e) None of these

ANSWER: A

Q36. The length of a rectangle is 42 cm which is 14 cm more than thediameter

of a circle. What is the area of the circle?
(a) 610 sq cm
(b) 676 sq cm
(c) 632 sq cm
(d) 616 sq cm
(e) None

ANSWER: D
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Q37. The area of the rectangle is 16 times the area of the square. If length of
the rectangle is 8 times the side of the square and breadth of the rectangle is24
cm, then find the side of the Square?
(a) 19
(b) 11
(c) 18
(d) 12
(e) 16

ANSWER:D

Q38. Four equal cubes are placed adjacently in a row. Find the ratio of total
surface area of the new cuboid to that of the sum of the surface areas of the
four cubes?
(a) 5:6
(b) 1:6
(c) 5:7
(d) 2:5
(e) 5:3

ANSWER: A
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Q39. The length and breadth of a playground are 36 m and 2l m respectively.

Poles are required to be fixed all along the boundary at a distance 3m apart. The
number of poles required will be?
(a) 39
(b) 38
(c) 37
(d) 40
(e) None of these

ANSWER: B

Q40. which value is more

1. Area of parallelogram with height and base is equal 8 and 10 respectively
2. Area of trapezium with parallel side is equal to 8 and 4 with height 8
3. Area of rhombus whose diagonals are 10 and 12 respectively?
(a) 1>2>3
(b) 3>2>1
(c) (3>1>2
(d) 2>1>3
(e) None of these

ANSWER: B

Level - 2
Q1. If the length of a rectangle is increased by 20% while the breadth of the
rectangle is decreased by 10% then find percentage change in area of the rectangle?
(a) 12% decreased
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(b)8% decreased
(c) 12% increased
(d)8% increased
(e) 21% decreased
ANS B
Solution:

Q2.The perimeter of a rectangle is 132 m and the difference between the length
and breadth of the rectangle is 14 m then find the perimeter of squarewhose area
is 16 m less than the area of the rectangle?
(a) 136m
(b)128m
(c) 114m
(d)92m
(e) None of these
ANS B
Solution:

Q3.The length and breadth of a rectangular piece of land are in the ratio of 3:
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2. The owner spent Rs. 3250 for fencing it from all the sides at the rate of Rs
6.50 per meter. The difference between length and breadth is?
(a) 50 m
(b)70 m
(c) 90 m
(d)85 m
(e) 65 m

ANS A
Solution:

Q4.The length of a rectangle is 12 m more than the side of the square and the
breadth of the rectangle is 5 m less than the side of the square. It the area of the
square is 784 Sq m. what is the area of the rectangle?
(a) 840 sq m(b)780
sq m
(c) 920 sq m(d)660
sq m
(e) None of these
ANS C
Solution:
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Q5.The area of a square is 1296 sq cm. Find the Perimeter of the rectangle, if length
is (1/3) the side of the square and breadth is 28 cm less than the side of the square?
(a) 40 cm
(b)52 cm
(c) 64 cm
(d)78 cm
(e) None of these
ANS A
Solution:

Q6.The radius of the circle is equal to seven-ninth of the side of the square.The
area of the circle is 1386 sq cm. Find the perimeter of a square?
(a) 124cm(b)112cm
(c) 108cm
(d)136cm
(e) None of these
ANS C
Solution:
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Q7.Find the volume of a cylinder, whose radius is half of the radius of a circle
having area 2464 cm2. Height of the cylinder is equal to the radius of the circle?
(a) 21452 cm3
(b)25786 cm3(c)
15344 cm3
(d)17248 cm3
(e) None of these
ANS D
Solution:

Q8.A ground is square in shape has a 18 metre wide road inside it runningalong
its sides. The area occupied by the road is 5292 sq.m. What is the perimeter
along the outer edge of the road?
(a) 620
(b)624
(c) 626
(d)622
(e) None of theseANS
Solution:
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Q9.The dimension of an open container is 100cm, 80cm, and 46 cm. Its thickness
is 6 cm. If 1 cubic cm of metal used in the box weight 1 gram, findthe weight of
the container?
(a) 125.64 kg
(b)126.65 kg
(c) 128.64 kg
(d)124.76 Kg
(e) None of these
ANS C
Solution:

Q10.A shape of rectangular block 18cm by 36cm by 45cm is cut up into equal cubes.
Find the least possible number of cubes?
(a) 40(b)20
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(c) 60
(d)30
(e) None of these
ANS A
Solution:

Q11.A hemispherical bowl contains milk of internal radius 36cm. This milk is to be
filled into cylindrical shaped bottles of diameter 12 cm and height 16cm. How many
bottles will be needed to empty the bowl?
(a) 54
(b)58
(c) 60
(d)45
(e) None of these
ANS A
Solution:
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Q12.The volume of a brick 1296 dm3.Its dimensions are in the ratio 3:2:1. Ifits
entire surface is painted at 50 paise per dm2 then cost will be?
(a) 367
(b)385
(c) 396
(d)350
(e) None of these
ANS C
Solution:

Q13.The diameter of the wheel of a van is 70 cm.How many circulations per

minute must the wheel make in order to keep a speed of 33 kmph?
(a) 150
(b)200
(c) 230
(d)250
(e) None of these
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ANS D
Solution:

Q14. Two centre piece circles form a compact disk. The inner and outer
circumferences of the CD are 10 4/7 and 15 6/7 respectively. Find the widthof the
CD?
(a) 0.84m
(b)0.74m
(c) 0.64m
(d)0.54m
(e) None of these
ANS A
Solution:
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Q15. The circumference of a circle is equal to the perimeter of a square whosearea

is 1089 sq cm. What is the area of the circle?
(a) 1386 sq cm
(b)1728 sq cm
(c) 1516 sq cm
(d)1644 sq cm
(e) None of these
ANS A
Solution:

Q16.What is the cost of covering a spherical bowl of radius 35 meters with a

golden sheet cover at the rate of Rs 1.5/m2?
(a) Rs.23300
(b)Rs.13400
(c) Rs.32700
(d)Rs.23100
(e) Rs.12700
ANS D
Solution:
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Q17. The length and the breadth of a rectangular plot are in the ratio of 7:5. If the
cost of fencing the plot (@ 25 per meter is Rs. 7200, what is the area of the plot?
(a) 6240
(b)3560
(c) 4560
(d)5040
(e) None of these
ANS D
Solution:

Q18.The total area of a circle and rectangle is 2058 Sq cm. The radius of the circle
is 21 cm. Find the perimeter of the rectangle, if breadth of the rectangleis 24 cm?
(a) 122 cm(b)136
cm
(c) 104 cm(d)148
cm
(e) None of these
ANS C
Solution:
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Q19.The circumference of the circle is 132 cm and the side of the square is
two-third of the radius of the circle. Find the perimeter of the square?
(a) 64 cm
(b)72 cm
(c) 56 cm
(d)48 cm
(e) None of these
ANS C
Solution:

Q20.The perimeter of a rectangle is 64 m and the difference between the

length and the breadth of the rectangle is 14 m then find the area or the
rectangle?
(a) 315 sq m(b)278
sq m
(c) 256 sq m(d)207
sq m
(e) None of these
ANS D
Solution:
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Q21.The ratio of the radii of two right circular cylinders (A and B) is 2: 5. The ratio of
the height of cylinders A to B is 3: 1. What is the ratio of the volumes of cylinders
A to B?
(a) 12:25
(b)9:25
(c) 9:20
(d)3:5
(e) 12:35
ANS A
Solution:

Q22. Smallest angle of a triangle is equal to two- third of the smallest angle ofa
quadrilateral. The ratio between the angles of the quadrilateral is 3:4.5:6.
Largest angle of the triangle is twice its smallest angle. What is the Sum ofsecond
largest angle of the triangle and largest angle of the quadrilateral?
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(a) 160˚
(b)180˚
(c) 190˚
(d)170˚
(e) 150˚
ANS B
Solution:

Q23. The circumference of a circle is equal to the perimeter of a square whosearea

is 484 sq cm what is the area of the circle?
(a) 676 sq.cm
(b)616 sq.cm
(c) 656 sq.cm(d)760
sq.cm
(e) None of these
ANS B
Solution:

Q24.The circumference of two circles is 132 metres and 176 metres respectively.
What is the difference between the area of the larger circle andthe smaller circle?
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(a) 1048 sq.metres

(b)1076 sq.metres
(c) 1078 sq.metres
(d)1090 sq.metres
(e) 1104 sq.metres
ANS C
Solution:

Q25.The length and the breadth of rectangular plot are in the ratio of 7:5. If the
cost of fencing the plot @ 25 per meter is Rs.7200, then find the area of the plot?
(a) 6240 sq meter
(b)3560 sq meter
(c) 4560 sq meter
(d)5040 sq meter
(e) None of these
ANS D
Solution:

Q26.The radius of a circle is more than the height of a right-angled triangle by40%.
The base of the right-angled triangle is 44 cm. If the area of the right- angled
triangle is equal to the area of the Circle, then what is the approximatearea of the
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circle?
(a) 79 sq.cm
(b)86 sq.cm
(c) 102 sq.cm(d)66
sq.cm
(e) Other than the given optionsANS A
Solution:

Q27.The angles of quadrilateral are in the ratio o 3:2:5:8. The second smallest
angle or quadrilateral is equal to second smallest angle of triangle. One of the
angles of triangle 3 equal to twice its smallest angle quadrilateral. Find the largest
angle of triangle
(a) 80˚
(b)60˚
(c) 100˚
(d)40˚
(e) None of these
ANS A
Solution:
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Q28.The perimeter of a rectangle is 52 m and the difference between the

length and the breadth of the rectangle is 10m then find the perimeter of
square whose area is equal to the area of the rectangle?
(a) 20(b)48
(c) 12
(d)30
(e) 50 ANS
B Solution:

Q29. The difference between length and breadth or the rectangle is 16. The
length of the rectangles equal to the side of the square, if the area or the
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square is 1024 Sq m. Find the perimeter the rectangle?

(a) 96m
(b)88m
(c) 74m
(d)112m
(e) None of these
ANS A
Solution:

Q30. The total area of a circle and rectangle 991 Sq cm The diameter of the circle
is 14 m. what is the sum of the circumference of Circle and perimeter ofrectangle,
if length o rectangle is 25 cm?
(a) 124 cm(b)168
cm
(c) 156 cm(d)142
cm
(e) None of these
ANS B
Solution:
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Q31. The area of a square is 784 sq cm whose side is 2 times of radius of acircle.
The circumference of the circle is equal to length of the rectangle, if perimeter of
rectangle is 300 cm. What is the breadth of rectangle?
(a) 56 cm
(b)62 cm
(c) 48 cm
(d)34 cm
(e) None of these
ANS B
Solution:

Q32.The difference between the length and breadth of the rectangle is 8. The
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perimeter of the rectangle is 64 m. find the area of the rectangle?

(a) 360 sq m(b)320
sq m
(c) 240 sq m(d)420
sq m
(e) None of these
ANS C
Solution:

Q33.Find the volume of a cylinder whose radius is half of the radius of a circle
having area 5544cm2. Height of the cylinder is double its radius.
(a) 48202cm3
(b)58212cm3
(c) 48212cm3
(d)58202cm3
(e) None of these
ANS B
Solution:

Q34. Area of a rectangle is equal to the area of a square, which is 484m^2.Thcratio

between the length and breadth of the rectangle is 7:3.If the cost of fencing per
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meter is Rs 5,what is the ratio between the total costs of fencing the rectangle to
that of the square?
(a) 5:4
(b)4:5
(c) 5:9
(d)4:9
(e) 6:5
ANS A
Solution:

Q35.A rectangular park has dimensions 200m X 8Om.A circular lawn is in the
middle of park. If the area of rectangular park leaving the circular lawn is 3526m2.
Then what is the Circumference of the circular lawn?
(a) 284
(b)484
(c) 396
(d)576
(e) 476
ANS C
Solution:

Q36.The sides of a rectangle cartons are in the ratio 2.3 and its area is486sq.m
find the perimeter of Rectangle?
(a) 75m
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(b)90m
(c) 124m
(d)82m
(e) None of these
ANS B
Solution:

Q37.The perimeter of a square is thrice the Perimeter of a rectangle. If the

perimeter of the square is 123 cm and the length of the rectangle is 11 cm, then
what is the difference between the breadth of the rectangle and the sideof the
square?
(a) 21.25cm
(b)21.89cm
(c) 54.12cm
(d)54.19cm
(e) 12.72cm
ANS A Solution:
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Q38. A gardener uses cylindrical roller of diameter 14 cm and length 35cm to

flatten a rectangular field of dimension 350cm *154cm. Find the number of
revolutions made by the roller to flatten the entire field?
(a) 35(b)45
(c) 76
(d)23
(e) 72 ANS
A Solution:

Q39. Three circles of radii 6cm, 8cm and 10cm touch each other pair was
externally. Find the area of the triangle formed by the line segments joiningthe
centres of the three circles?
(a) 45√3
(b)48√5
(c) 48√3
(d)42√3
(e) 46√5
ANS B
Solution:

Q40.A hemispherical bowl of internal diameter 54 cm contains a liquid. This liquid

is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. Howmany
bottles are required to empty the bowl?
(a) 162
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(b)172
(c) 142
(d)145
(e) None of these
ANS A
Solution: