CBSE Class 9 Mathematics Surface Areas And Volumes Worksheet Set D

Question. Sonali has about half a litre of molten wax to make a candle. Which of these candles could she have made using the entire quantity of wax? (1 cm³ = 1ml)

Answer : B

Question. Zubin wants to cover the CURVED SURFACE of an old waste paper basket with coloured paper. The dimensions of the basket are shown below.  What is the total area that has to be covered with paper?

(a) 220 cm²
(b) 440 cm²
(c) 880 cm²
(d) 1760 cm²

Answer : C

Question. Travelling only along the edges and covering a distance of exactly 22 cm, how many different routes can be taken to go from corner P to corner Q of this cuboid?

(a) 10
(b) 8
(c) 6
(d) 1

Answer : C

Question. The formula for calculating the area of the walls of a rectangular room, A is given as:
A = 2h (l + b), where h is the height of the room. l its lenght and b its breadth
Which of the following would be the correct formula to find the breadth of a room when the area, height and length are given?
(a) A - 2hl
(b) A-l/2h
(c) -2h/A-l
(d) A/2h - l

Answer : D

Question. A piece of cardboard is cut to the shape shown and 2 dots are marked on it. The cardboard is then folded along the lines to form a CUBE. Which of the cubes shown here CAN be constructed from the cardboard piece?

Answer : A

Question. What is the length of tape required to cover the entire outer CURVED surface of the pipe shown below if the width of the tape used is 2 cm? (Assume that there is no overlap of tape)

(a) 22 cm
(b) 25 cm
(c) 7.7 m
(d) 11 m

Answer : D

Question. The cuboid shown below consists of 9 cubes of side 1 unit each. If the shaded unit cube is REMOVED, what will be the surface area of the remaining solid?

(a) 24 sq. units
(b) 28 sq. units
(c) 30 sq. units
(d) 32 sq. units

Answer : C

Question. 250 ml of water is poured into a container like the one shown below which already contains some water. Assuming that no water spills out, what will be the increase in the level of water in the container? (1 ml = 1 cm3)

(a) 2. 5 cm
(b) 5 cm
(c) 10 cm
(d) We can't say

Answer : A

Question. A solid cylinder made of pure metal has a mass of 24 kg. What would the mass be if it were twice as thick but only half as long?

(a) 12 kg
(b) 24 kg
(c) 36 kg
(d) 48kg

Answer : D

Question. A cube of side 1 metre is stuck on top of another cube of side 2 metres, which in turn is stuck on top of a cuboid of dimensions (6 m x 5 m x 3 m)  to form the solid shown below. The entire exposed surface of this solid (including the bottom of the cuboid) has to be painted. How many square metres is that?

(a) 151
(b) 146
(c) 120
(d) 113

Answer : B

Question. Two squares of sides 4 cm and one square of side 5 cm are placed as shown. The shaded area is:

(a) 37 cm²
(b) 41 cm²
(c) 45 cm²
(d) 57 cm²

Answer : C

Question. The piece below is cut out from a circular sheet of radius 21 cm. What is the area of the piece?

(a) 23.1 cm²
(b) 231 cm²
(c) 346.5 cm²
(d) 441 cm²

Answer : B

Question. The floor of a room that is 6 m long and 4 m 20 cm wide has to be tiled entirely with square tiles OF EQUAL SIZE. What is the MINIMUM number of square tiles with which this can be done? (No tile can be broken or cut)
(a) 30
(b) 42
(c) 60
(d) 70

Answer : D

Question. In the grid shown below, the distance between any two consecutive points marked on OP (or OQ) is taken to be the unit distance. Which point on the grid is at a distance of 5 units from O?

(a) A
(b) B
(c) C
(d) D

Answer : C

Question. Points P, Q and R are co-planar. In which of the following cases will they NECESSARILY be collinear?
(a) When PQ = PR
(b) When PQ + PR > QR
(c) When PQ + QR = PR
(d) When PR < PQ + QR

Answer : C

Question. The radius of a sphere (in cm) whose volume is 12π cm³, is 
(a) 3
(b) 3√3
(c) 32/3
(d) 31/3
Answer : C

Question. If the surface area of a sphere is 144π, then its radius is
(a) 6 cm
(b) 8 cm
(c) 12 cm
(d) 10 cm
Answer : A

Question. The edge of a cube whose volume is equal to that of a cuboid of dimensions 8 cm × 4 cm × 2 cm is
(a) 6 cm
(b) 4 cm
(c) 2 cm
(d) 8 cm
Answer : B

Question. If the radii of two spheres are in the ratio 2 : 3, then the ratio of their respective volumes is
(a) 8 : 27
(b) 3 : 5
(c) 7 : 24
(d) 5 : 14
Answer : A

Question. The edge of a cube whose volume is 8x3 is
(a) x
(b) 2x
(c) 4x
(d) 8x
Answer : B

Question. If the volume of a 7 cm high right circular cylinder is 448π cm3, then its radius is equal to
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm
Answer : D

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm².
Reason (R): If r be the radius and h be the height of the cylinder, then total surface area = (2πrh + 2πr²).
Answer : A

Question. Assertion (A): If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.
Reason (R): If r is the radius and h the height of the cone, then slant height = √h² + r² .
Answer : A

Answer the following.

Question. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
Answer : (2/3) πr³ = 3πr²         ⇒ r = 9/2 units
∴ d = 9 units

Question. Total surface area of a cube is 216 cm². Find its volume. 
Answer : 6l² = 216 ⇒ l² = 36
⇒ l = 6
∴ Volume of cube = l³ = (6)³ = 216 cm³

Question. If a solid right-circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere, find the radius of the sphere.
Answer : Volume of cone = volume of sphere
∴ (1/3)π6² × 24 = (4/3)πr³
⇒ 864 = 4r³
⇒ r3 = 216
⇒ r = 6 cm
So, radius of sphere = 6 cm

Question. Find the curved surface area of a right-circular cone of height 15 cm and base diameter 16 cm. 
Answer : Slant height of cone, l = √8² + 15²
(∵ Diameter = 16 cm)
⇒ l = 17 cm
∴ CSA of cone = πrl = π × 8 × 17
= 136 p cm²

Question. Find the radius of the sphere whose surface area is 36 π cm².
Let r be the radius of sphere.
Then, 4πr² = 36π
⇒ r² = 36π/4π = 9
⇒ r = 3 cm

Question. 12 solid spheres of the same radii are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. Find the diameter of the each sphere
πR²H = 12 x 4/3 πr³
1 × 1 × 16 = 4/3 × r³ × 12
r³ = 1³
r = 1
d = 2 cm

Case Study Based Questions

I. Adventure camps are the perfect place for the children to practise decision making for themselves without parents and teachers guiding them every move. Some students of a school reached for adventure at Sakleshpur. At the camp, the waiters served some students with a welcome drink in a cylindrical glass while some students in a hemispherical cup whose dimensions are shown below. After that they went for a jungle trek. The jungle trek was enjoyable but tiring. As
dusk fell, it was time to take shelter.

Each group of four students was given a canvas of area 551 m². Each group had to make a conical tent to accommodate all the four students. Assuming that all the stitching and wasting incurred while cutting, would amount to 1 m², the students put the tents. The radius of the tent is 7 m.

Question. The volume of cylindrical cup is
(a) 295.75 cm³
(b) 7415.5 cm³
(c) 384.88 cm³
(d) 404.25 cm³
Answer : D

Question. The volume of hemispherical cup is
(a) 179.67 cm³
(b) 89.83 cm³
(c) 172.25 cm³
(d) 210.60 cm³
Answer : B

Question. Which container had more juice and by how much?
(a) Hemispherical cup, 195 cm³
(b) Cylindrical glass, 207 cm³
(c) Hemispherical cup, 280.85 cm³
(d) Cylindrical glass, 314.42 cm³
Answer : D

Question. The height of the conical tent prepared to accommodate four students is
(a) 18 m
(b) 10 m
(c) 24 m
(d) 14 m
Answer : B

Question. How much space on the ground is occupied by each student in the conical tent
(a) 54 m²
(b) 38.5 m²
(c) 86 m²
(d) 24 m²
Answer : C

<1M>

1.Find the area enclosed between two concentric circles of radii 4 cm and 3 cm.

2.A cuboid has total surface area of 40 sq m and its lateral surface area is 26 sq m. Find the area of base.

3.The area of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that

4.A sphere is double height as the cube The ratio of their volume is:

(A) B) C) (D)

5.The lateral surface area of a right circular cylinder with base radius 8m & height 14m is:

(A) 714 sq m B) 724 sq m C) 704 sq m D) None

6.The number of surfaces in right circular cylinder is:

(A) 3 B) 2 C) 4 D) 1

7.A sphere and a cube are of the same height. The ratio of their volume is-

(A) 11:21 B) 21:11 C) 3:4 D) 4:3

8.A cylindrical rod whose height is 8 times of its radius, is melted and recast into spherical balls of same

radius. The no. of balls will be:

(A) 4 B) 3 C) 6 D) 8

9.The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. The

length of wire is ....

(A) 3600 cm B) 360 cm C) 36 cm D) None

10.The height and radius of a cone are 3 cm and 4 cm respectively. Its surface area is-

(A) 12 cm2 B) 6 cm2 C) cm2 D) cm2

11.The ratio of the volume & surface area of a sphere of unit radius is-

(A) 1:3 B) 4:3 C) 3:1 D) 3:4

12.Curved surface area of an ice-cream cone of slant height 12 cm is 113.04 cm2. Find the base radius?

(take = 3.14)

(A) 1 cm B) 2 cm C) 3 cm D) None

13.The height of a right circular cone is 16 cm & its base radius is 12 cm. Find the curved surface area.

(take = 3.14)

(A) 755 cm2 (B) 753.6 cm2 (C) 750 cm2 (D) None

14.The radius of the cylinder whose lateral surface area is 704 cm2 & height is 8 cm is:

(A) 14 cm (B) 4 cm (C) 6 cm (D) 8 cm

15.The radius of a cylinder is doubled but its lateral surface area is unchanged. Then its height must be-

(A) Doubled. (B) Constant. (C) Halved. (D) Trippled.

Please click the below link to access CBSE Class 9 Mathematics Worksheet - Surface Areas and Volumes (2)