# Volume and Surface Areas Quiz Set 016

### Question 1

A cuboid block of wood 8 × 16 × 8 is horizontally placed on a table. Then another cube of side 8 is placed on this block. How much surface area is exposed to air?

A

768 sq. units.

B

770 sq. units.

C

766 sq. units.

D

772 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 × 82 = 768 sq. units.

### Question 2

What is the radius of a sphere if the ratio of volume to the surface area is 23 : 17?

A

$4{1/17}$ units.

B

$5{3/8}$ units.

C

$2{14/19}$ units.

D

$6{6/19}$ 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 = ${69/17}$, which is same as: $4{1/17}$.

### Question 3

How much water flows per hour through a pipe of radius 7 cm, if water flows at 10 km/h?

A

49 π cu. m.

B

51 π cu. m.

C

47 π cu. m.

D

53 π cu. m.

Soln.
Ans: a

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is π × ${7 × 7 × 10 × 1000}/{100 × 100}$, which can easily be cancelled to get 49π cu. m.

### Question 4

The slant height of a right conical tent of height 15 m is 17 m. What is the curved surface area?

A

136 π sq. m.

B

137 π sq. m.

C

135 π sq. m.

D

138 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = $√{17^2 - 15^2}$ = $√{289 - 225}$ = 8. The volume is π × r × l = π × 8 × 17 = 136π sq. m.

### Question 5

A cone of height 6 cm and radius of base 12 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

6 cm.

B

8 cm.

C

4 cm.

D

10 cm.

Soln.
Ans: a

Let the radius of the sphere be R. The volumes are equal. So $4/3$ π R3 = $1/3$ π 122 × 6. Cancelling π/3 from both sides, R3 = ${12 × 12 × 6}/4$ = 216 = 63. So R = 6 cm.