CBSE Class 9 Mathematics Surface Areas And Volumes Worksheet Set D

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

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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)