ICSE Class 10
MATHEMATICS
MENSURATION
PYQs from 2010-2023
MENSURATION
1. A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone
of height 4 cm. The solid is immersed completely in a cylindrical container
filled with water to a certain height. If the radius of the cylinder is 14 cm, find
the rise in the water level.
[2023]
2. Volume of a cylinder of height 3 cm is 48 π. Radius of the cylinder is:
(a) 48 cm
(b) 16 cm
(c) 4 cm
(d) 24 cm [2023]
3. A solid cone of radius 5 cm and height 9 cm is melted and made into small
cylinders of radius of 0.5 cm and height 1.5 cm. find the number of cylinders
so formed. [2022 Semester-2]
4. The radius of a roller 100 cm long is 14 cm. The curved surface area of the
roller is: (Take π = 22/7)
(a) 13200 cm2
(b) 15400 cm2
(c) 4400 cm2
(d) 8800 cm2 [2022 Semester-2]
5. A solid wooden cylinder is of radius 6cm and height 16cm. Two cones each of
radius 2cm and height 6cm are drilled out of the cylinder. Find the volume of
the remaining solid. Take π = 22/7 [2022 Semester-2]
6. The volume of a conical tent is 462 m³ and the area of the base is 154 m².
The height of the cone is:
(a) 15 m
(b) 12 m
(c) 9 m
(d) 24 m [2022 Semester-2]
7. From a solid wooden cylinder of height 28 cm and diameter 6 cm, two conical
cavities are hollowed out. The diameters of the cones are also of 6 cm and
height 10.5 cm. Taking π = 22/7 find the volume of the remaining solid.
[2020]
8. A solid spherical ball of radius 6 cm is melted and recast into 64 identical
spherical marbles. Find the radius of each marble. [2020]
9. A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder
of height 32 cm. Find the : [4]
(i) radius of the cylinder
(ii) curved surface area of the cylinder [Take π = 3.1] [2019]
10. A hemispherical and conical hole is scooped out of a solid wooden cylinder.
Find the volume of the remaining solid where the measurements are as
follows: [4]
The height of the solid cylinder is 7 cm,
radius of each of hemisphere, cone and
cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest
whole number. [Take π = 22/7]
[2019]
11. The circumference of the base of a cylindrical vessel is 132 cm and its height
is 25 cm. Find the:
(i) radius of the cylinder
(ii) volume of cylinder, (use π = 227) [3] [2018]
12. The following figure represents a solid consisting of a right circular cylinder with a
hemisphere at one end and a cone at the other. Their common radius is 7. The
height of the cylinder and cone are each of 4 cm. Find the volume of the solid. [4]
[2018]
13. A conical tent is to accommodate 77 persons. Each person must have 16𝑛3 of air
to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its
curved surface area. [3] [2017]
14. A certain number of metallic cones, each of radius 2 cm and height 3 cm are
melted and recast into a solid sphere of radius 6 cm. Find the number of cones. [3]
[2016]
15. Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of
height 8 cm. Find the radius of the cone so formed. [3] [2015]
16. The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast
into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate :
(i) the radius of the sphere.
(ii) the number of cones recast. (Take π = 22/7) [4] [2014]
17. A solid sphere of radius 15 cm is melted and recast into solid right circular cones
of radius 2.5 cm and height 8 cm. Calculate the number of cones recast. [2013]
18. A hollow sphere of internal and external radii 6 cm and 8 cm respectively is
melted and recast into small cones of base radius 2 cm and height 8 cm. Find the
number of cones. [3] [2012]
19. A solid cone of radius 5 cm and height 8 cm is melted and made into small
spheres of radius 0.5 cm. Find the number of spheres formed. [2011]
20. A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate
sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height
of the cone. [3] [2010]
ANSWERS
1. 1.5 cm
2. (c)
3. 200
4. (d)
5. 1760 cm3
6. (c)
7. 594 cm3
8. 1.5 cm
9. 3 cm ; 595.2 cm2
10. 113 cm3
11. 21 cm ; 34650 cm3
12. 1540 cm3
13. 24 m ; 550 m2
14. 72
15. 6 cm
16. 14 cm ; 128
17. 270
18. 37
19. 400
20. 4.05 cm
-----------------------------------------------------------------------
