MENSURATION – 3D
The edge of a cube is 12 cm. Find:
(a)Volume
(b)Curved Surface Area
(c) Total Surface Area
(d)Diagonal
If diagonal of a cube is 𝟏𝟐 cm, then find its volume.
a) 8 cms3
b) 12 cms3
c) 16 cms3
d) 24 cms3
The total surface area of a cube is 864 cms2. Find its volume.
a) 729 cms3
b) 1728 cms3
c) 1440 cms3
d) 1500 cms3
Three cubes of edge 3 cm, 4 cm and 5 cm are melted to form a new
cube. What is the edge of the new cube?
a) 6 cm
b) 8 cm
c) 9 cm
d) 10 cm
Three cubes, having edge 1 cm, 6 cm and 8 cm, are melted to form
a new cube. What is the diagonal of the new cube?
a) 9 3 cm
b) 10 3 cm
c) 12 3 cm
d) 15 3 cm
The dimensions of a cuboid are 16 cm, 18 cm and 24 cm. Find:
(a)Volume
(b)Curved Surface Area
(c) Total Surface Area
(d)Diagonal
Twenty cubes each of edge 2 cm are placed one above the other.
Find the total surface area of the cuboid so formed.
a) 229 cms2
b) 328 cms2
c) 540 cms2
d) 400 cms2
The three edges of a rectangular solid are 36 cm, 75 cm and 80 cm,
respectively. Find the edge of the cube of the same capacity.
a) 40 cm
b) 48 cm
c) 60 cm
d) 75 cm
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, then find the
total surface area of the cube.
a) 72 cm3
b) 216 cm3
c) 432 cm3
d) 108 cm3
The lateral surface area of a cylinder is 1056 cm2 and its height is
equal to 16 cm. What is its volume?
a) 5544 cms3
b) 6828 cms3
c) 7240 cms3
d) 8560 cms3
What is the amount of concrete required to build a cylindrical pillar
whose base has a perimeter of 8.8 m and whose curved surface
area is 17.6 m2?
a) 10.48 m3
b) 12.32 m3
c) 14.40 m3
d) 11.65 m3
The heights of two cylinders are in the ratio of 3:1. If the volumes of
two cylinders be same, find the ratio of their respective radii.
a) 1 : 2
b) 1 : 3
c) 3 : 1
d) 2 : 5
The circumference of the base of a right circular cone is 220 cm and
its height is 84 cm. Find the curved surface area of the cone.
a) 8650 cms2
b) 10010 cms2
c) 12480 cms2
d) 9640 cms2
Find the volume of the largest right circular cone that can be cut out
of a cube of edge 7 cm.
a) 89.83 cms3
b) 96.75 cms3
c) 76.47 cms3
d) 92.81 cms3
How many metres of cloth 10 m wide is required to make a conical
tent with base radius of 14 m and height 48 m?
a) 196 m
b) 245 m
c) 220 m
d) 200 m
The volume of a conical tent is 1232 m3 and the area of its base is
154 m2. Find the length of a 2 m wide canvas required to build the
tent.
a) 270 m
b) 272 m
c) 275 m
d) 276 m
Find the surface area of a sphere having radius 3.5 cm.
a) 140 cms2
b) 178 cms2
c) 154 cms2
d) 132 cms2
A spherical ball of radius 6 cm is melted and recast into three
spherical balls. The radii of two of these spherical balls are 3 cm and
4 cm. What is the radius of the third ball.
a) 3 cm
b) 4 cm
c) 4.5 cm
d) 5 cm
The base of a right circular cone has the same radius ‘r’ as that of a
sphere. If both the sphere and the cone have the same volume, then
which of the following will be the height of the cone?
a) 3r
b) 4r
7𝑟
c)
4
7𝑟
d)
3
The diameter of a hemisphere is 7 cm. Find its:
(a)Volume
(b)Curved Surface Area
(c) Total Surface Area
If a sphere and a hemisphere have the same total surface area, find
the ratio of their radii.
a) 1 : 2
b) 1 : √3
c) √3 : 2
d) 2 : √5
