Sheet

04
Mensuration - 3D
Type - 11
Hemisphere/
 22 
 take π =
 

1. The radius of a hemisphere is 21 cm. Find the  7 
curved surface area of the hemisphere.

 22 
π =
 

 7 
(a) 2790 (b) 2700 (c) 2772 (d) 2730
2. The diameter of a hemisphere is 28 m. Find the
total surface area of the hemisphere. (a) 531.11m³ (b) 331.14 m³
(c) 452.57 m³ (d) 562.18 m³
[SSC GD - 2023]

(a) 1800 (b) 2100 (c) 1848 (d) 2048 7. A spherical melon of radius 9 cm is cut into two
equal hemispheres. Find the volume of each hemi-
3. If the total surface area of a hemisphere is 115.5 sphere (in cm³, rounded off to two decimal places).
m², what is the radius of the hemisphere?
 22 
 take π =
 

 7 

5 7 9 cm
(a) (b) (c) 7 (d) 5 (cm³
2 2
4. The diameter of a hemisphere is 6 cm. What will  22 
be the ratio of the values of its curved surface area π =
 

 7 
and total surface area?
6 cm (a) 1,527.43 cm³ (b) 1,547.34 cm³
(c) 1,472.53 cm³ (d) 1,372.35 cm³
[SSC GD - 2022]
(a) 2 : 3 (b) 1 : 2 (c) 3 : 5 (d) 1 : 3
Type - 12
[SSC GD - 2022]
Cone/
5. The radius of a hemisphere is 21 cm. Its volume
1. If the radius of the base and slant height of a cone
 22  are 13 cm and 35 cm respectively, then what will
 takeπ =
(in cm³) is:  
 be the curved surface area of the cone?
 7 
13 cm
35 cm
 22  (a) 1484 cm² (b) 1470 cm²
π = 

 7 
(c) 1440 cm² (d) 1430 cm²
(a) 19404 (b) 22101 (c) 21109 (d) 20112 [SSC GD - 2022]

[SSC GD - 2023] 2. The curved surface area of a right circular cone is

6. A sphere of radius 6 m is cut into two equal parts. 3185 π cm². If the radius of its base is 35 cm, then
Find the volume of each hemisphere thus formed. what is its height (in cm)?

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 3185 π cm²
35 cm (cm (a) 729 m³ (b) 924 m³
(c) 970 m³ (d) 616 m³
8. The heights of two cones are in the ratio 2 : 1 and
(a) 42 (b) 84 (c) 49 (d) 98
the ratio of their radii is 1 : 2. Find the ratio of their
[SSC GD - 2021] volumes./
3. The area of the base of a right circular cone is 81 π
cm² and its height is 18 cm. Find its slant height.
(a) 4 : 3 (b) 1 : 2 (c) 2 : 1 (d) 3 : 4
81 π cm²
[SSC GD - 2021]
18 cm
9. The volumes of two cones are in the ratio 3 : 2 and
(a) 15 5 cm (b) 21 cm their radii are in the ratio 3 : 4. What is the ratio of
their heights?
(c) 24 cm (d) 9 5 cm
[SSC GD - 2021]
4. The ratio of radius and slant height of a cone is 5 :
(a) 8 : 3 (b) 9 : 4 (c) 4 : 9 (d) 2 : 1
7 respectively. If its curved surface area is 1,760
[SSC GD - 2022]
 22  Mensuration – 3D
 takeπ =
cm², find its radius.  

 7  Miscellaneous
1. Three cubes, each of side 5 cm, are joined together
in a second-to-second order. What is the total sur-
cm² face area of the resulting cuboid?
 22  5 cm
π =
 
 7 
(a) 24 cm (b) 20 cm (c) 28 cm (d) 21 cm
(a) 325 cm² (b) 375 cm²
[SSC GD - 2022]
(c) 350 cm² (d) 380 cm²
7 [SSC GD – 2022]
5. The radius of the base of a right circular cone is
2 2. How many cubes of side 4 cm can be formed by
and height is 12 m. Find its volume. melting a solid metal cuboid of length 12 cm, breadth
8 cm and height 8 cm?/
7
2

(a) 11 (b) 14 (c) 12 (d) 13

(a) 160 m³ (b) 144 m³
[SSC GD – 2023]
(c) 154 m³ (d) 140 m³ 3. The surface area of a solid cube is 726 cm². It is
6. The radius of the base of a cone is 14 m and the melted to form a solid cylinder whose radius is 11
slant height is 25 m. Find the volume of the cone. cm. What is the height (in cm) of the cylinder?
 22 
 takeπ =
 

 7 
(a) 1142 m³ (b) 1132 m³
726 cm²
(c) 1232 m³ (d) 1542 m³
11 cm (cm
7. The area of the base of a cone is 154 m² and height
is 18 m then what is its volume?  22 
π =
 

 7 

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 (a) 5.5 (b) 1.9 (c) 3.5 (d) 2.5 5. A cone of radius 9 cm and height 15 cm is melted to
form a cylinder of height 45 cm. The diameter of
[SSC GD - 2021]
the cylinder is.
4. A spherical ball of radius 3 cm is immersed in wa-
9 cm 15 cm 45
ter filled in a vertical cylinder of radius 5 cm. As-
suming that the ball is completely immersed in cm
water, find the rise in the water level (in cm, up to
(a) 3 cm (b) 5 cm (c) 10 cm (d) 6 cm
two decimal places).
[SSC GD - 2022]
3 cm 5 cm

cm

(a) 1.44 (b) 2.25 (c) 3.14 (d) 1.75

[SSC GD - 2021]

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4 FOLLOW RAKESH YADAV SIR ON SOCIAL MEDIA