Grade 9 : Mathematics - 13. Surface Area/Volume (Set 3)

Question 1

The edges of a cuboid are in the ratio $1:2:3$ and its total surface area is $88cm^2$. What is the volume of the cuboid?

Accepted Answer

C) $48cm^3$

Answer

A) $24cm^3$

Answer

B) $36cm^3$

Answer

D) $64cm^3$

Answer

E) $96cm^3$

Question 2

If the length of the main diagonal of a cube is $6\sqrt{3}cm$, what is its total surface area?

Accepted Answer

C) $216cm^2$

Answer

A) $108cm^2$

Answer

B) $144cm^2$

Answer

D) $288cm^2$

Answer

E) $324cm^2$

Question 3

The curved surface area of a right circular cylinder is $264m^2$ and its volume is $924m^3$. Find the height of the cylinder. (Take $\pi = \frac{22}{7}$)

Accepted Answer

C) 6 m

Answer

A) 4 m

Answer

B) 5 m

Answer

D) 7 m

Answer

E) 8 m

Question 4

A right circular cone has a slant height of 25 cm and a base radius of 7 cm. Find the volume of the cone. (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) $1232cm^3$

Answer

A) $1120cm^3$

Answer

C) $1344cm^3$

Answer

D) $1456cm^3$

Answer

E) $1568cm^3$

Question 5

If the radius of a sphere is increased by 50%, by what percentage does its surface area increase?

Accepted Answer

C) 125%

Answer

A) 50%

Answer

B) 100%

Answer

D) 150%

Answer

E) 225%

Question 6

The total surface area of a solid hemisphere is $462cm^2$. Find its radius. (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) 7 cm

Answer

A) 3.5 cm

Answer

C) 10.5 cm

Answer

D) 14 cm

Answer

E) 21 cm

Question 7

A water storage tank of length 10 m, width 8 m, and height 6 m needs to be plastered on the inside floor and four inner walls. What is the total cost at ₹15 per $m^2$?

Accepted Answer

C) ₹4440

Answer

A) ₹3600

Answer

B) ₹4240

Answer

D) ₹5120

Answer

E) ₹5880

Question 8

A metallic solid sphere of radius 6 cm is melted and recast into a solid cylinder of radius 8 cm. What is the height of the cylinder?

Accepted Answer

C) 4.5 cm

Answer

A) 3.5 cm

Answer

B) 4.0 cm

Answer

D) 5.0 cm

Answer

E) 5.5 cm

Question 9

Two cylinders have radii in the ratio $2:3$ and heights in the ratio $5:3$. What is the ratio of their volumes?

Accepted Answer

B) $20:27$

Answer

A) $10:9$

Answer

C) $4:9$

Answer

D) $8:27$

Answer

E) $5:9$

Question 10

A conical tent is 9 m high with a base radius of 12 m. Find the cost of canvas required to make the tent at ₹70 per $m^2$. (Take $\pi = \frac{22}{7}$)

Accepted Answer

C) ₹39,600

Answer

A) ₹35,200

Answer

B) ₹38,400

Answer

D) ₹41,200

Answer

E) ₹42,800

Question 11

The volume of a cube is $512cm^3$. What is its total surface area?

Accepted Answer

C) $384cm^2$

Answer

A) $256cm^2$

Answer

B) $320cm^2$

Answer

D) $448cm^2$

Answer

E) $512cm^2$

Question 12

A hemispherical bowl has an inner radius of 10.5 cm. How many liters of liquid can it hold? (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) 2.4255 L

Answer

A) 1.213 L

Answer

C) 3.638 L

Answer

D) 4.851 L

Answer

E) 5.120 L

Question 13

A solid wooden rectangular block of dimensions $30cm imes 20cm imes 10cm$ is cut into smaller cubes of edge 5 cm. How many such cubes can be formed?

Accepted Answer

C) 48

Answer

A) 24

Answer

B) 36

Answer

D) 60

Answer

E) 72

Question 14

A cone and a cylinder have equal circular bases and equal heights. If the volume of the cylinder is $180cm^3$, what is the volume of the cone?

Accepted Answer

C) $60cm^3$

Answer

A) $30cm^3$

Answer

B) $45cm^3$

Answer

D) $90cm^3$

Answer

E) $120cm^3$

Question 15

If the surface area of a sphere is $616cm^2$, what is its diameter? (Take $\pi = \frac{22}{7}$)

Accepted Answer

C) 14 cm

Answer

A) 7 cm

Answer

B) 10.5 cm

Answer

D) 21 cm

Answer

E) 28 cm

Question 16

A hollow cylindrical pipe has outer radius 5 cm, inner radius 2 cm, and height 14 cm. Find the volume of metal used in making the pipe. (Take $\pi = \frac{22}{7}$)

Accepted Answer

C) $924cm^3$

Answer

A) $462cm^3$

Answer

B) $693cm^3$

Answer

D) $1155cm^3$

Answer

E) $1386cm^3$

Question 17

The ratio of the radius to the slant height of a cone is $3:5$. If its curved surface area is $135\picm^2$, find its base radius.

Accepted Answer

B) 9 cm

Answer

A) 6 cm

Answer

C) 12 cm

Answer

D) 15 cm

Answer

E) 18 cm

Question 18

A hollow hemispherical bowl has an inner radius of 6.5 cm and steel thickness of 0.5 cm. Find the outer curved surface area of the bowl. (Take $\pi = \frac{22}{7}$)

Accepted Answer

C) $308cm^2$

Answer

A) $154cm^2$

Answer

B) $231cm^2$

Answer

D) $462cm^2$

Answer

E) $616cm^2$

Question 19

A metallic cuboid of dimensions $16cm imes 12cm imes 9cm$ is melted and recast into a single solid cube. Find the edge length of the cube.

Accepted Answer

C) 12 cm

Answer

A) 8 cm

Answer

B) 10 cm

Answer

D) 14 cm

Answer

E) 16 cm

Question 20

The surface areas of two spheres are in the ratio $16:25$. What is the ratio of their volumes?

Accepted Answer

C) $64:125$

Answer

A) $16:25$

Answer

B) $32:50$

Answer

D) $256:625$

Answer

E) $4:5$

Grade 9 : Mathematics - 13. Surface Area/Volume (Set 3)