Mensuration 3D TSA

and CSA Part-1

 1.) A cistern 6 m long and 4 m wide,
contains water up to a depth of 1 m 25
cm. The total area of the wet surface is

A.) 55 m 2
B.) 53 .5 m 2
C.) 50 m 2
D.) 49 m 2
 2.) If the height of a cylinder is
increased by 15 per cent and the radius
of its base is decreased by 10 per cent
then by what per cent will its curved
surface area change ?

A.) 3.5 per cent decrease

B.) 3.5 per cent increase
C.) 5 per cent increase
D.) 5 per cent decrease
 3.) A right circular conical structure stands
on a circular base of 21 metre diameter and
is 14 metre in height. The total cost of colour
washing for its curved surface at Rs 6 per
square metre is
 22 
 take   
 7 

A.) Rs 4365
B.) Rs 4465
C.) Rs 3465
D.) Rs 3365
 4.) Water flows through a cylindrical pipe,
whose radius is 7 cm, at 5 metre per second.
The time, it takes to fill an empty water
tank, with height 1.54 metres and area of
base ( 3 X 5 ) square metres,
 22 
 take   
 7 

A.) 6 minutes
B.) 5 minutes
C.) 10 minutes
D.) 9 minutes
 5.) A solid cylinder has total surface area of
462 sq.cm. Its curved surface area is 1/3rd of
the total surface area. Then the radius of the
cylinder is

A.) 7 cm
B.) 3.5 cm
C.) 9 cm
D.) 11 cm
6.) The diameter of a cylinder is 7 cm and its
height is 16 cm. Using the value of   22
7
The lateral surface area of the cylinder is

A.) 352 cm 2
B.) 350 cm 2
C.) 355 cm 2
D.) 348 cm 2
 7.) The height of a solid right circular
cylinder is 6 metres and three times the sum
of the area of its two end faces is twice the
area of its curved surface. The radius of its
base ( in metre) is

A.) 4
B.) 2
C.) 8
D.) 10
 8.) The height of a circular cylinder is
increased six times and the base area is
decreased to one-ninth of its value. The
factor by which the lateral surface of the
cylinder increases is
A.) 2
1
B.) 2
2
C.)
3
3
D.)
2
9.) The radius and height of a cylinder are in
the ratio. 5 : 7 and its volume is 550cm3.
Calculate its curved surface area in sq.cm.

A.) 110
B.) 444
C.) 220
D.) 616
10.) The area of the curved surface and the
area of the base of a right circular cylinder
are a square cm and b square cm
respectively. The height of the cylinder is

2a
A.) cm
b
a b
B.) cm
2 
a
C.) cm
2 b
a 
D.) cm
2 b
11.) Find the length of the largest rod that
can be placed in a room of
2
16 m long, 12 m broad and 10 m high.
3

A.) 23 m
B.) 68 m
2
C.) 22 m
3
1
D.) 22 m
3
12.) If the volume of two cubes are in the
ratio 27 : 64, then the ratio of their total
surface area is :

A.) 27:64
B.) 3 : 4
C.) 9 : 16
D.) 3 : 8
13.) Find the length of the longest rod that
can be placed in a hall of 10 m length, 6 m
breadth and 4 m height.

A.) 2 38 m
B.) 4 38 m
C.) 2 19 m
D.) 19 m
 14.) The volume of a cuboid is twice the
volume of a cube. If the dimensions of the
cuboid are 9 cm, 8 cm and 6 cm, the total
surface area of the cube is :

A.) 72 cm2
B.) 216cm2
C.) 432cm2
D.) 108cm2
 15.) The length, breadth and height of a
room is 5 m, 4 m and 3m respectively. Find
the length of the largest bamboo that can be
kept inside the room

A.) 5m
B.) 60 m
C.) 7m
D.) 5 2m
 16.) The length of the longest rod that can
be placed in a room which is 12 m long, 9 m
broad and 8 m high is

A.) 27 m
B.) 19 m
C.) 17 m
D.) 13 m
 17.) A cube of edge 5 cm is cut into cubes
each of edge of 1 cm. The ratio of the total
surface area of one of the small cubes to
that of the large cube is equal to :

A.) 1 : 125
B.) 1 : 5
C.) 1 : 625
D.) 1 : 25
18.) The perimeter of the floor of a room is
18 m. What is the area of the walls of the
room, if the height of the room is 3 m ?

A.) 21m2
B.) 42 m2
C.) 54 m2
D.) 108m2
 19.) The length ( in metres) of the longest
rod that can be put in a room of dimensions
10 m  10 m  5 m is

A.) 15 3
B.) 15
C.) 10 2
D.) 5 3
 20.) The floor of a room is of size 4 m 3 m
and its height is 3m . The walls and ceiling of
the room require painting. The area to be
painted is

A.) 66 m2
B.) 54 m2
C.) 43 m2
D.) 33 m2
21.) If the sum of three dimensions and the
total surface area of a rectangular box are 12 cm
2
and 94cm respectively, then the maximum
length of a stick that can be placed inside
the box is
A.) 5 5 cm
B.) 5 cm
C.) 6 cm
D.) 2 5 cm
22.) If the length of the diagonal of a cube is
8 3 cm , then its surface area is

A.) 192cm2
B.) 512cm2
C.) 768cm2
D.) 384cm2
 23.) The area of the four walls of a room is
660 m 2 and its length us twice its breadth.
If the height of the room is 11 m , then area
of its floor (in m 2 ) is

A.) 120
B.) 150
C.) 200
D.) 330
24.) The maximum length of a pencil that
can be kept in a rectangular box of
dimensions 8 cm  6 cm  2 cm is

A.) 2 13 cm
B.) 2 14 cm
C.) 2 26 cm
D.) 10 2 cm
 25.) The volume of a cubical box is 3.375
cubic metres. The length of edge of the box
is

A.) 75 cm
B.) 1.5 m
C.) 1.125 m
D.) 2.5 m
26.) Diagonal of a cube is 6 3 cm . Ratio of
its total surface area and volume
(numerically) is

A.) 2 : 1
B.) 1 : 6
C.) 1 : 1
D.) 1 : 2
27.) The length of the largest possible
rod that can be placed in a cubical
room is 35 3 m . The surface area
of the largest possible sphere that
fit within the cubical room
 22 
 assume    (in square m) is
 7 

A.) 3,500
B.) 3,850
C.) 2,450
D.) 4,250
 28.) The volume of air in a room is 204 m.3
The height of the room is 6 m . What is the
floor area of the room ?

A.) 32 m2
B.) 46 m2
C.) 44 m2
D.) 34 m2
 29.) The slant height of a conical mountain
is 2 .5 km and the area of its base is1 . 54 km 2 .
Taking   22 , the height of the
7
mountain is :

A.) 2.2 km
B.) 2.4 km
C.) 3 km
D.) 3.11 km
30.) The base of a conical tent is 19.2 metres
in diameter and the height of its vertex is 2.8
meters. The area of the canvas required to
put up such a tent ( in square metres)
 22 
 taking    is nearly.
 7 

A.) 3017.1
B.) 3170
C.) 301.7
D.) 30.17
 31.) If S denotes the area of the curved
surface of a right circular cone of height h
and semi-vertical angle  then S equals

A.)  h tan 
2 2

B.) 1  h 2 tan 2 
3
C.)  h sec  tan 
2

D.) 1  h 2 sec  tan 

3
 32.) The height and the radius of the base of
a right circular cone are 12 cm and 6 cm
respectively. The radius of the circular cross-
section of the cone cut by a plane parallel to
its base at a distance of 3 cm from the base is
A.) 4 cm
B.) 5.5 cm
C.) 4.5 cm
D.) 3.5 cm
 33.) The radius of base and slant height of a
cone are in the ratio 4 : 7 . If its curved
surface area is 792 cm 2, then the radius
(in cm) of its base is
 22 
 use ,   
 7 

A.) 8
B.) 12
C.) 14
D.) 16
 34.) A semi-circular sheet of metal of
diameter 28 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
 35.) If curved surface area of a cylinder is
1386 sq cm and height is 21 cm, what will be
its radius ?
 22 
 take ,   
 7 

A.) 21 cm
B.) 5.25 cm
C.) 10.5 cm
D.) 15.75 cm
36.) A right angled sector of radius ‘r’ cm is
rolled up into a cone in such a way that the
two binding radii are joined together. Then
the curved surface area of the cone is

A.)  r 2 cm 2
B.) 4  r 2 cm 2
C.)  r 2 2
cm
4
D.) 2  r 2 cm 2
 37.) The radius of the base of a conical tent
is 16 metre . If 427 3 sq . m . canvas is required to
7
construct the tent, then the slant height of
the tent is :
 22 
 taking   
 7 
A.) 17 metre
B.) 15 metre
C.) 19 metre
D.) 8.5 metre
 38.) The volume of a right circular cone
is 1232cm3 and its vertical height is 24 cm . Its
curved surface area is

A.) 154 cm 2
B.) 550 cm 2
C.) 604 cm 2
D.) 704 cm 2
 39.) If h , c , v are respectively the
height, curved surface area and volume of a
right circular cone, then the value of
3 vh3  c 2 h 2  9v 2 is

A.) 2
B.) -1
C.) 1
D.) 0
40.) If the radius of a sphere is increased by
2 cm , it surface area increased 352cm2 .
The radius of the sphere before change is :

 22 
 taking   
 7 
A.) 3 cm
B.) 4 cm
C.) 5 cm
D.) 6 cm
 41.) Spheres A and B have their radii 40 cm
and 10 cm respectively. Ratio of surface area
of A to the surface area of B is :

A.) 1 : 16
B.) 4 : 1
C.) 1 : 4
D.) 16 : 1
42.) The volume of a sphere is 88  (14)3 cm3..
21
The curved surface of the sphere is
 22 
 take p  
 7 

A.) 2424 cm 2

B.) 2446 cm 2

C.) 2484 cm 2

D.) 2464 cm 2
43.) The surface area of a sphere is 64 cm.2 .
Its diameter is equal to

A.) 16 cm
B.) 8 cm
C.) 4 cm
D.) 2 cm
 44.) 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
C.) 3 : 2
D.) 18 : 25
45.) When the circumference of a toy ballon
is increased from 20 cm to 25 cm, its radius
(in cm) is increased by :

A.) 5
B.) 5

C.) 5
2

D.)
5
46.) The height and the total surface area of
a right circular cylinder are 4 cm and 8  sq.cm.
respectively. The radius of the base of
cylinder is

A.) ( 2 2  2 ) cm
B.) ( 2  2 ) cm
C.) 2 cm
D.) 2 cm
47.) The ratio of the surface area of a sphere
and the curved surface area of the cylinder
circum-scribing the sphere is

A.) 1 : 2
B.) 1 : 1
C.) 2 : 1
D.) 2 : 3
 48.) The total surface area of a metallic
hemisphere is 1848cm2. The hemisphere is
melted to form a solid right circular cone. If
the radius of the base of the cone is the
same as the radius of the hemisphere, its
height is
A.) 42 cm
B.) 26 cm
C.) 28 cm
D.) 30 cm
 49.) If the radii of two spheres are in the
ratio 1 : 4, then their surface area are in the
ratio :

A.) 1 : 2
B.) 1 : 4
C.) 1 : 8
D.) 1 : 16
50.) A solid metallic sphere of radius 8 cm is
melted to form 64 equal small solid spheres.
The ratio of the surface area of this sphere
to that of a small sphere is

A.) 4 : 1
B.) 1 : 16
C.) 16 : 1
D.) 1 : 4
1 2 3 4 5 6 7 8 9 10
D C B B A A A A C C
11 12 13 14 15 16 17 18 19 20
C C A B D C D C B B
21 22 23 24 25 26 27 28 29 30
A D C C B C B D B C
31 32 33 34 35 36 37 38 39 40
C C B B C C D B D D
41 42 43 44 45 46 47 48 49 50
D D B B C A B C D C