# Volume and Surface Areas Quiz Set 010

### Question 1

What is the length of an edge of a cube if the ratio of volume to the total surface area is 41 : 23?

A

\$10{16/23}\$ units.

B

\$12{5/22}\$ units.

C

\$8{23/25}\$ units.

D

\$12{3/5}\$ 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\$ = \${246/23}\$, which is same as: \$10{16/23}\$.

### Question 2

A room has a floor size of 17 × 43 sq. m. What is the height of the room if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

A

\$12{11/60}\$ m.

B

\$13{24/59}\$ m.

C

\$10{51/62}\$ m.

D

\$14{43/62}\$ m.

Soln.
Ans: a

Let h be the height, and l and b be the length and breadth. We are given lb + lb = lh + hb + lh + hb. Combining the terms and cancelling 2, we get lb = h(l + b), which gives h = \${lb}/{l + b}\$ = \${17 × 43}/{17 + 43}\$ = \${731/60}\$, which is same as: \$12{11/60}\$ m.

### Question 3

How many boxes measuring 1 m × 1m × 1 m should be dropped into a water tank 6 m × 8 m so that the water level rises by 1 m?

A

48 .

B

50 .

C

46 .

D

52 .

Soln.
Ans: a

The volume of water to be displaced is 6 × 8 × 1 cu. m. This should be equal to the volume of the boxes to be dropped. So N × 1 × 1 × 1 = 6 × 8 × 1, which gives N = 6 × 8 = 48.

### Question 4

How much water flows per hour through a pipe of radius 49 cm, if water flows at 10 km/h? Take π = 22/7.

A

7546 cu. m.

B

7548 cu. m.

C

7544 cu. m.

D

7550 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 \${22 × 49 × 49 × 10 × 1000}/{7 × 100 × 100}\$, which can easily be cancelled to get 7546 cu. m.

### Question 5

The areas of three adjacent faces of a cube are 2, 3 and 6. It's volume is?

A

6 cu. units.

B

8 cu. units.

C

4 cu. units.

D

10 cu. units.

Soln.
Ans: a

Let the sides be L, B and H. Then LB = 2, BH = 3 and LH = 6. Multiplying all three of them L2B2H2 = (2 × 3 × 6) = 36 = 62, which gives LBH = 6 = volume of the cuboid. 