# Volume and Surface Areas Quiz Set 014

### Question 1

What is the weight of a hollow cylindrical pipe 49 cm long, and having internal and external radii as 4 and 6 cm? The pipe is made of a metal of density 2 gm/cc. Take π = 22/7.

A

6160 gm.

B

6162 gm.

C

6158 gm.

D

6164 gm.

Soln.
Ans: a

The volume of the pipe is π × (62 - 42) × 49, which is \$22/7\$ × 20 × 49. Weight = vol × density = \$22/7\$ × 20 × 49 × 2 = 6160 gm.

### Question 2

What is the volume of a cone generated by rotating a right angled triangle with sides 41, 9 and 40 cm? The rotation is done about the side of length 40 cm.

A

1080 π sq. cm.

B

1081 π sq. cm.

C

1079 π sq. cm.

D

361 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 9 cm, and height h = 40 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(9^2 × 40)\$ = 1080π.

### Question 3

A cone of height 2 cm and radius of base 4 cm is made up of modeling clay. A child reshapes it in the form of a sphere. What is the radius of the sphere?

A

2 cm.

B

4 cm.

C

8 cm.

D

6 cm.

Soln.
Ans: a

Let the radius of the sphere be R. The volumes are equal. So \$4/3\$ π R3 = \$1/3\$ π 42 × 2. Cancelling π/3 from both sides, R3 = \${4 × 4 × 2}/4\$ = 8 = 23. So R = 2 cm.

### Question 4

A cuboid block of wood 7 × 14 × 7 is horizontally placed on a table. Then another cube of side 7 is placed on this block. How much surface area is exposed to air?

A

588 sq. units.

B

590 sq. units.

C

586 sq. units.

D

592 sq. units.

Soln.
Ans: a

Let the dimensions of the cuboid be L, 2L and L. Its total surface area is 2(L × 2L + 2L × L + L × L) = 10L2. When it is placed on the table, the bottom face is hidden, so net visible area is 10L2 - 2L2 = 8L2. When the cubical block of side L is placed on this block its(i.e., cube's) own L2 and L2 of the cuboidal block is hidden. So it hides 2L2. Thus, the net visible is 8L2 + 6L2 - 2L2 = 12L2 = 12 × 72 = 588 sq. units.

### Question 5

What is the volume of rain water collected in a right cylindrical can of radius 8 cm, if 3 cm rainfall is recorded in the city?

A

192 π cu. cm.

B

194 π cu. cm.

C

190 π cu. cm.

D

196 π cu. cm.

Soln.
Ans: a

The height of the can will be filled to 3 cm. The volume of collected water is same as the volume of cylinder with radius 8 cm and height 3 cm., which equals π82 × 3 = 192π cu. cm. This Blog Post/Article "Volume and Surface Areas Quiz Set 014" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-11