# Volume and Surface Areas Quiz Set 009

### Question 1

A room has a floor size of 17 × 31 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

\$10{47/48}\$ m.

B

\$12{11/47}\$ m.

C

\$9{29/50}\$ m.

D

\$13{21/50}\$ 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 × 31}/{17 + 31}\$ = \${527/48}\$, which is same as: \$10{47/48}\$ m.

### Question 2

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

A

100 π cu. m.

B

102 π cu. m.

C

98 π cu. m.

D

104 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 × \${10 × 10 × 10 × 1000}/{100 × 100}\$, which can easily be cancelled to get 100π cu. m.

### Question 3

What is the volume of a cone generated by rotating a right angled triangle with sides 25, 7 and 24 cm? The rotation is done about the side of length 24 cm.

A

392 π sq. cm.

B

393 π sq. cm.

C

391 π sq. cm.

D

\$131{2/3}\$ π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 7 cm, and height h = 24 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(7^2 × 24)\$ = 392π.

### Question 4

What is the length of a 10 mm wire that has been drawn out of a lump of 77 cu. cm. tin? Take π = 22/7.

A

2450 cm.

B

2452 cm.

C

2448 cm.

D

2454 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\$ = 77, which gives L = \${10 × 10 × 77 × 7}/22\$ = 2450 cm.

### Question 5

An iron tank 2 m × 3 m is filled with water upto a height of 2 m. What surface area of the tank is at a higher risk of corrosion?

A

26 cu. m.

B

28 cu. m.

C

24 cu. m.

D

30 cu. m.

Soln.
Ans: a

If L, B and H are the dimensions of the water column, then the wet area is 2(BH + LH) + LB = 2 × (3 × 2 + 2 × 2) + 2 × 3. The result is 26 cu. m. This Blog Post/Article "Volume and Surface Areas Quiz Set 009" 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