MATHEMATICS WORKSHEET
SURFACE AREA AND VOLUME- CLASS 9
Basic level
1. A cuboidal water tank is 6m long, 5 m wide and 4.5 m deep. How many litres of water can it be hold? (1 m3 = 1000 litres).
(Ans. 135000 litres)
2. Find the radius and volume of a sphere whose surface area is 154 cm2.
(Ans. radius = 3.5 cm and volume = 179𝟐𝟑 𝒄𝒎𝟑)
3. Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
(Ans. 165 cm2).
4. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of sheet is required for the same? (Ans. 7.48 m2)
5. How many planks each of which is 2 m long, 3 cm broad and 4 cm thick can be cut-off from a wooden block 6 m long, 18 cm broad and 44 cm thick?
(Ans. 198).
6. Curved surface area of a cone is 306 cm2 and its slant height is 14 cm. Find (i) radius of the base (ii) total surface area of the cone
(Ans. r = 7cm and TSA = 462 cm2)
7. The radius and slant height of a cone are in the ratio 4:7. If its curved surface area is 792 cm2, find its radius. (Ans. r = 12 cm)
8. The lateral surface area of a cube is 576 cm2. Find its volume and total surface area.
(Ans. Volume = 1728 cm3 and TSA = 864 cm2)
Intermediate level
9. A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface area of the solid so formed.
10. The resident of society decided to paint the hall of cancer detective center in their premises. If the floor of the cuboidal hall has a perimeter equal to 260 m and height 6 m then
a. Find the cost of painting of its four walls at the rate of Rs. 9 per m2.
b. What is the amount contributed by 50 people?
c. Which value is depicted by the residents?
11. A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 am and 6 cm respectively. Find the volume of the copper used in making the pipe.
(Ans. V= 10560 cm3)
12. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.
(Ans. 20:27, 10:9)
13. The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314
cm3, find the slant height and the radius.(Use 𝜋 = 3.14)
(Ans. = 13m, 5m)
14. How many spherical bullets can be made out of a solid cube of lead whose edge measures
44 cm, each bullet being 4 cm in diameter?
(Ans. 2541)
15. Find the volume of the largest right circular cone that can be cut out of a cube whose
edge is 9 cm.
(Ans. 190.93 cm3)
16. A solid cylinder has a total surface area 462 cm2. Its curved surface area is one-third of
the total surface area. Find the volume of the cylinder.
(Ans. 539 cm3)
17. A rectangular sheet of paper 30 cm x 18 cm can be transformed into the curved surface
area of a right circular cylinder into two ways either by rolling the paper along its length
or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus
formed.
(Ans. 5:3)
18. The volume of metallic cylinder pipe is 748 cm3. Its length is 14 cm and its external
radius is 9 cm. Find its thickness. (Ans. thickness of the pipe = 1 cm)
Advanced level
19. The diameter of a sphere is decreased by 25%. By what percent its surface area
decreased? (Ans. 43.75%)
20. If V is the volume of a cuboid of dimensions l, b, h and S is its surface area, then prove
that
V
1
=
S
2




 
l b h
1 1 1
.
21. A cone of height 24 cm has a curved surface area 550 cm2. Find its volume.
(Ans. volume = 1232 cm3)
22. The surface area of a sphere of radius 5 cm is five times the curved surface area of a cone
of radius 4 cm. Find the height and volume of the cone.
(Ans. height = 3 cm and volume = 50.29 cm2)
23. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all
around to a width of 5 m to form an embankment. Find the height of embankment.
(Ans. 4.66 m)
24. The volume of the two spheres are in the ratio 64:27. Find the difference of their surface
areas, if the sum of their radii is 7cm.
(Ans. 88 cm2)
25. A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find
the depth and capacity of cup.
(Ans. Depth = 12.12 cm, Capacity = 622.26 cm3)