The document provides information about mensuration and calculating volumes and surface areas of different geometric solids like cubes, spheres, cylinders, cones, and prisms. It includes definitions of these shapes, formulas to calculate their measurements, sample problems, and a practice test with multiple choice questions related to volumes and surface areas of combinations of solids.

1. 10. Mensuration

2. 10. Mensuration
Page 2
Mensuration
1. The volume of the solid formed by joining two basic solids is the sum of the volumes of the
constituents.
2. In calculating the surface area of combinations of solids, we can’t add the surface area of the
two constituents, because some part of the surface area disappears in the process of joining
them.
Sl.No.
Name of the
Solid
Figure
Lateral/curved
surface area
Total surface
area
Volume Nomenclature
1 Cuboid l= length
b= breadth
2 Cube
a= side of the
cube
3 Right Prism
Perimeter of
base X height
Lateral surface
area +2(area
of the end
surface)
Area of the
base X height
4
Regular
circular
cylinder
r= radius of
the base
5
Right
circular
cylinder
r= radius of
the base
h= height
l= slant
height
6
Right
pyramid
(perimeter of
base)X slant
height
Lateral surface
area+ area of
the base
(perimeter of
base)X height
7 Sphere r= radius
8 Hemisphere r= radius

3. 10. Mensuration
Page 3
Multiple choice Questions
1. The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 2mm. The
length of the wire is
(a) (b)18m (c)36m (d)66m
2. A solid sphere of radius “r” is melted and cast into the shape of a solid cone of height r, then the
radius of the base of the cone is
(a) (b) (c) (d)
3. The curved surface area of a cylinder is and its volume is The ratio of its
diameter to its height
(a) (b)7:3 (c)6:7 (d)7:6
4. A cylinder with base radius 8cm and height 2cm is melted to form a cone of height 6cm. The
radius of the cone is
(a) (b)5cm (c)6cm (d)8cm
5. If three metallic spheres of radii 6cm, 8cm and 10cm are melted to form a single sphere, the
diameter of the sphere is
(a)12 (b)24cm (c)30cm (d)36cm
6. The volumes of two spheres are in the ratio64:27. The ratio of their surface areas is
(a)1 (b)2:3 (c)9:16 (d)16:9
7. The surface area of a sphere is same as the curved surface area of a right circular cylinder
whose height and diameter are 12cm each. The radius of the sphere is
(a)3 (b)4cm (c)6cm (d)12cm
8. 12 spheres of the same size are made from melting a solid cylinder of 16cm diameter and 2cm
height. The diameter of each sphere is
(a) (b)2cm (c)3cm (d)4cm
9. A solid piece of iron of dimensions 49X33X24 cm is molded into a sphere. The radius of the
sphere is
(a)21 (b)28cm (c)35cm (d)None
10. The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is
(a) (b) (c) (d)
11. The radii of two cylinders are in the ratio 3:5. If their heights are in the ratio 2:3. Then the ratio
of their curved surface areas is
(a)2 (b)5:2 (c)2:3 (d)3:5
12. The curved surface area of right circular cone of height is 15cm and its diameter is 16cm is
(a) (b) (c) (d)
13. A right circular cylinder of radius and height just encloses sphere of diameter
(a) (b) (c) (d)2h

4. 10. Mensuration
Page 4
14. If four times the sum of the areas of two circular faces of a cylinder of height 8cm is equal to
twice the curved surface area, then diameter of the cylinder is
(a)4 (b)8cm (c)2cm (d)6cm
15. A metallic sphere of radius 10.5cm is melted and then recast into small cones, each of radius
3.5cm and height 3cm. The number of such cones is
(a)63 (b)126 (c)21 (d)130
16. An oil drum is in the shape of a cylinder having the following dimensions; diameter 2m and
height is 7m. The painter charges Rs.3/- per to paint the drum. Then the total charges to
be paid to the painter for 10 drums
(a)Rs.1508/- (b) Rs.1507/- (c) Rs.1506/- (d)None
17. A sphere, a cylinder and a cone are of the same radius and same height. Then ratio of their
curved surface areas is
(a)1:2:3 (b)2:2: (c)4:4: (d)130
18. A company wanted to manufacture 100 hemispherical basins from thin steel sheet. If the
radius of hemispherical basin is 21cm, then the required area of steel sheet to manufacture the
basins.
(a) (b) (c) (d)
19. A joker’s cap is in the form of right circular cone whose base radius is cm and height is cm
Then the area of the sheet required to make 20 such caps.
(a) (b) (c) (d)
20. A cylinder and cone have bases of equal radii and are of equal heights. Then their volumes are
in the ratio is
(a)1 (b)1:2 (c)3:1 (d)None
21. A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the
height of the cone are6cm and 4cm respectively. Then the surface area of the toy is _______
(a)105 (b)103.62 (c)104.12 (d)None
22. Two cubes each of volume 32 are joined end to end together. Then the total surface area of
the resulting cuboid
(a) (b) (c) (d)
23. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends.
The length of the capsule is 14mm and the width is 5mm. Then its surface area is
(a)22 (b) (c) (d)
24. The volume of the largest right circular cone that can be cut out of a cube whose edge is 7cm
(a) (b) (c) (d)
25. A cone of height 24cm and radius of base 6cm is made up of modelling clay. A child reshapes it
in the form of a sphere. Find the radius of the sphere.
(a)4 (b)5cm (c)6cm (d)2cm

5. 10. Mensuration
Page 5
26. The number of silver coins, 1.75cm in diameter and thickness 2mm, need to be melted to form
a cuboid of dimensions 5.5cmX10cmX3.5cm
(a)150 (b)120 (c)140 (d)130
27. A solid metallic sphere of diameter 28cm is melted and recast into a number of smaller cones,
each of diameter and height 3cm. Then the number of cones so formed.
(a)675 (b)674 (c)671 (d)672
28. Three metal cubes with edges 15cm, 12cm and 9cm respectively are melted together and
formed in a simple cube. Then the edge of this cube is
(a)14cm (b)18cm (c)12cm (d)14cm
29. A golf ball has diameter equals to 4.1cm. Its surface has 150 dimples which are in
hemispherical shape of radius 2mm. Then the total surface area which is exposed to the
surroundings. =___________
(a)40.85 (b)43.40 (c)84.21 (d)None
30. The number of spherical balls can be made out of a solid cube of lead whose edge measures
44cm and each ball being 4cm in diameter.
(a)2500 (b)2501 (c)2541 (d)None
Answers
1 2 3 4 5 6 7 8 9 10
c a b d b d c d a b
11 12 13 14 15 16 17 18 19 20
a d c b b a c b d c
21 22 23 24 25 26 27 28 29 30
b c a b c a d b a c