# Volume and Surface Areas Quiz Set 006

### Question 1

What is the length of an edge of a cube if the ratio of volume to the total surface area is 31 : 41?

A

\$4{22/41}\$ units.

B

\$5{27/40}\$ units.

C

\$3{16/43}\$ units.

D

\$7{8/43}\$ units.

Soln.
Ans: a

The well-known relation for a cube is \$S/V = 6/a\$, which can be re-arranged to get \$a = 6 × V/S\$ = \${186/41}\$, which is same as: \$4{22/41}\$.

### Question 2

A cuboid block of wood 5 × 10 × 5 is horizontally placed on a table. Then another cube of side 5 is placed on this block. How much surface area is exposed to air?

A

300 sq. units.

B

302 sq. units.

C

298 sq. units.

D

304 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 × 52 = 300 sq. units.

### Question 3

What is the length of a 10 mm wire that has been drawn out of a lump of 33 cu. cm. tin? Take π = 22/7.

A

1050 cm.

B

1052 cm.

C

1048 cm.

D

1054 cm.

Soln.
Ans: a

The wire is a cylinder with r = 1/10 cm, and length L. The volume of tin is equal to the volume of the wire. So π \${1/10} × {1/10} × L\$ = 33, which gives L = \${10 × 10 × 33 × 7}/22\$ = 1050 cm.

### Question 4

What is the weight of a hollow cylindrical pipe 56 cm long, and having internal and external radii as 13 and 15 cm? The pipe is made of a metal of density 9 gm/cc. Take π = 22/7.

A

88704 gm.

B

88706 gm.

C

88702 gm.

D

88708 gm.

Soln.
Ans: a

The volume of the pipe is π × (152 - 132) × 56, which is \$22/7\$ × 56 × 56. Weight = vol × density = \$22/7\$ × 56 × 56 × 9 = 88704 gm.

### Question 5

When a weight W kg. is kept on a 3 m × 8 m boat floating over a lake, it sinks by 3 cm. What is W, if the density of water is 1000 kg/cu. m?

A

720 kg.

B

722 kg.

C

718 kg.

D

724 kg.

Soln.
Ans: a

The weight W is equal to the weight of water displaced by it. So W = \${3 × 8 × (3/100)}\$ × 1000 = 720 kg. 