# Volume and Surface Areas Quiz Set 011

### Question 1

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 2

What is the length of a 10 mm wire that has been drawn out of a lump of 88 cu. cm. tin? Take π = 22/7.

A

2800 cm.

B

2802 cm.

C

2798 cm.

D

2804 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\$ = 88, which gives L = \${10 × 10 × 88 × 7}/22\$ = 2800 cm.

### Question 3

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

A

\$3{15/41}\$ units.

B

\$4{19/40}\$ units.

C

\$2{11/43}\$ units.

D

\$6{3/43}\$ 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\$ = \${138/41}\$, which is same as: \$3{15/41}\$.

### Question 4

A room has a floor size of 47 × 29 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

\$17{71/76}\$ m.

B

\$19{14/75}\$ m.

C

\$16{1/2}\$ m.

D

\$20{31/78}\$ 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}\$ = \${47 × 29}/{47 + 29}\$ = \${1363/76}\$, which is same as: \$17{71/76}\$ m.

### Question 5

What is the volume of rain water collected in a right cylindrical can of radius 1 cm, if 7 cm rainfall is recorded in the city?

A

7 π cu. cm.

B

9 π cu. cm.

C

5 π cu. cm.

D

11 π cu. cm.

Soln.
Ans: a

The height of the can will be filled to 7 cm. The volume of collected water is same as the volume of cylinder with radius 1 cm and height 7 cm., which equals π12 × 7 = 7π cu. cm. 