# Volume and Surface Areas Quiz Set 005

### Question 1

The slant height of a right conical tent of height 9 m is 41 m. What is the curved surface area?

A

1640 π sq. m.

B

1641 π sq. m.

C

1639 π sq. m.

D

1642 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = $√{41^2 - 9^2}$ = $√{1681 - 81}$ = 40. The volume is π × r × l = π × 40 × 41 = 1640π sq. m.

### Question 2

What is the weight of a hollow cylindrical pipe 42 cm long, and having internal and external radii as 13 and 15 cm? The pipe is made of a metal of density 3 gm/cc. Take π = 22/7.

A

22176 gm.

B

22178 gm.

C

22174 gm.

D

22180 gm.

Soln.
Ans: a

The volume of the pipe is π × (152 - 132) × 42, which is $22/7$ × 56 × 42. Weight = vol × density = $22/7$ × 56 × 42 × 3 = 22176 gm.

### Question 3

What is the volume of a right cone whose cross-section is an isosceles triangle with base 32 cm and slant height 34 cm?

A

2560 π sq. cm.

B

2561 π sq. cm.

C

2559 π sq. cm.

D

$854{1/3}$ π sq. cm.

Soln.
Ans: a

One of the right triangles of the isosceles triangle has its base = 32/2 = 16. By Pythagorean theorem, the height = $√{34^2 - 16^2}$ = $√{1156 - 256}$ = 30. The radius of the base of the cone r = 16 cm, and height h = 30 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(16^2 × 30)$ = 2560π.

### Question 4

What is the radius of a sphere if the ratio of volume to the surface area is 31 : 41?

A

$2{11/41}$ units.

B

$3{7/20}$ units.

C

$1{9/43}$ units.

D

$5{1/43}$ units.

Soln.
Ans: a

Let R be the radius. Then $V/S = {4/3 × \text"π" × R^3}/{4 × \text"π" × R^2}$ = $R/3$, so R = 3 × ratio = ${93/41}$, which is same as: $2{11/41}$.

### Question 5

What is the volume of rain water collected in a right cylindrical can of radius 8 cm, if 4 cm rainfall is recorded in the city?

A

256 π cu. cm.

B

258 π cu. cm.

C

254 π cu. cm.

D

260 π cu. cm.

Soln.
Ans: a

The height of the can will be filled to 4 cm. The volume of collected water is same as the volume of cylinder with radius 8 cm and height 4 cm., which equals π82 × 4 = 256π cu. cm.