Grade 9 : Mathematics - 13. Surface Area/Volume (Set 4)

Question 1

The dimensions of a rectangular cuboid are in the ratio $4:3:2$. If its total surface area is $1300cm^2$, what is the volume of the cuboid?

Accepted Answer

B) $3000cm^3$

Answer

A) $2500cm^3$

Answer

C) $3200cm^3$

Answer

D) $3600cm^3$

Question 2

A solid right circular cylinder has a base radius of 7 cm and a height of 10 cm. What is its total surface area? (Take $\pi = \frac{22}{7}$)

Accepted Answer

A) $748cm^2$

Answer

B) $616cm^2$

Answer

C) $440cm^2$

Answer

D) $880cm^2$

Question 3

A right circular cone has a base radius of 6 cm and a vertical height of 8 cm. Find its total surface area in terms of $\pi$.

Accepted Answer

C) $96\picm^2$

Answer

A) $60\picm^2$

Answer

B) $80\picm^2$

Answer

D) $100\picm^2$

Question 4

Calculate the volume of a solid metallic sphere whose radius is 21 cm. (Take $\pi = \frac{22}{7}$)

Accepted Answer

A) $38808cm^3$

Answer

B) $19404cm^3$

Answer

C) $29106cm^3$

Answer

D) $41200cm^3$

Question 5

What is the ratio of the Curved Surface Area (CSA) to the Total Surface Area (TSA) of a solid hemisphere of radius $r$?

Accepted Answer

B) $2:3$

Answer

A) $1:2$

Answer

C) $3:4$

Answer

D) $4:5$

Question 6

A solid wooden cube with an edge length of 12 cm is melted and recast into 8 identical smaller solid cubes. What is the edge length of each smaller cube?

Accepted Answer

C) 6 cm

Answer

A) 3 cm

Answer

B) 4 cm

Answer

D) 8 cm

Question 7

A hollow cylindrical metallic pipe has an inner radius of 4 cm, an outer radius of 5 cm, and a length of 20 cm. Find the volume of metal used to construct the pipe in terms of $\pi$.

Accepted Answer

C) $180\picm^3$

Answer

A) $140\picm^3$

Answer

B) $160\picm^3$

Answer

D) $200\picm^3$

Question 8

A right circular conical funnel has a base radius of 5 cm and a slant height of 13 cm. What is the volume of the funnel in terms of $\pi$?

Accepted Answer

A) $100\picm^3$

Answer

B) $120\picm^3$

Answer

C) $60\picm^3$

Answer

D) $300\picm^3$

Question 9

A hemispherical bowl has an inner radius of 9 cm. What is the maximum volume of liquid it can hold in terms of $\pi$?

Accepted Answer

B) $486\picm^3$

Answer

A) $243\picm^3$

Answer

C) $729\picm^3$

Answer

D) $972\picm^3$

Question 10

Storage Box	Length ($l$)	Breadth ($b$)	Height ($h$)
Box A	10 cm	10 cm	10 cm
Box B	20 cm	5 cm	10 cm
Box C	25 cm	4 cm	10 cm

Based on the table above, all three boxes have equal volume ($1000cm^3$). Which box requires the greatest Surface Area to Volume ratio ($ ext{TSA}/V$)?

Accepted Answer

C) Box C

Answer

A) Box A

Answer

B) Box B

Answer

D) All three boxes have equal surface area

Question 11

A wooden toy consists of a cone surmounted on a hemisphere of the same radius 3.5 cm. The total height of the combined toy is 15.5 cm.

Find the total surface area of the toy. (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) $214.5cm^2$

Answer

A) $198cm^2$

Answer

C) $231cm^2$

Answer

D) $254.5cm^2$

Question 12

Water flows at the rate of 15 km/h through a cylindrical pipe of internal diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide.

How much time will it take for the level of water in the tank to rise by 21 cm?

Accepted Answer

B) 2 hours

Answer

A) 1.5 hours

Answer

C) 2.5 hours

Answer

D) 3 hours

Question 13

If the radius of a solid sphere is doubled, by what percentage does its surface area increase?

Accepted Answer

C) 300%

Answer

A) 100%

Answer

B) 200%

Answer

D) 400%

Question 14

The ratio of the base radius to the height of a solid cylinder is $2:3$. If its volume is $1617cm^3$, find its total surface area. (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) $770cm^2$

Answer

A) $616cm^2$

Answer

C) $840cm^2$

Answer

D) $924cm^2$

Question 15

A conical tent is 10 m high and its base radius is 24 m. Find the cost of canvas required to make the tent at $₹70 ext{ per m}^2$. (Take $\pi = \frac{22}{7}$)

Accepted Answer

B) ₹137,280

Answer

A) ₹120,500

Answer

C) ₹145,000

Answer

D) ₹152,400

Question 16

A metallic spherical shell of internal and external radii 3 cm and 5 cm is melted and recast into a solid right cylinder of diameter 14 cm. What is the height of the cylinder?

Accepted Answer

B) 2.67 cm

Answer

A) 1.75 cm

Answer

C) 3.50 cm

Answer

D) 4.25 cm

Question 17

A spherical hollow rubber ball has an outer diameter of 12 cm and an inner diameter of 8 cm.

Find the volume of rubber in the ball. (Use $\pi = 3.14$)

Accepted Answer

B) $636.37cm^3$

Answer

A) $512.45cm^3$

Answer

C) $718.20cm^3$

Answer

D) $804.12cm^3$

Question 18

Storage Box	Length ($l$)	Breadth ($b$)	Height ($h$)
Box A	10 cm	10 cm	10 cm
Box B	20 cm	5 cm	10 cm
Box C	25 cm	4 cm	10 cm

Comparing the two cylindrical water tanks above, which statement is mathematically true regarding their storage capacities?

Accepted Answer

C) Both tanks have identical storage capacity

Answer

A) Tank X has greater capacity than Tank Y

Answer

B) Tank Y has greater capacity than Tank X

Answer

D) Tank X holds twice as much volume as Tank Y

Question 19

A rectangular hall measures 12 m in length, 9 m in width, and 8 m in height. What is the length of the longest straight rod that can fit inside the hall?

Accepted Answer

C) 17 m

Answer

A) 15 m

Answer

B) 16 m

Answer

D) 18 m

Question 20

A spherical ball of radius 3 cm is placed snugly inside a cubic box of side length 6 cm. Find the volume of empty space left inside the box. (Use $\pi = 3.14$)

Accepted Answer

C) $102.96cm^3$

Answer

A) $88.54cm^3$

Answer

B) $96.20cm^3$

Answer

D) $113.04cm^3$

Grade 9 : Mathematics - 13. Surface Area/Volume (Set 4)