# Volume and Surface Areas Quiz Set 017

### Question 1

A room has a floor size of 13 × 37 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

\$9{31/50}\$ m.

B

\$10{41/49}\$ m.

C

\$8{15/52}\$ m.

D

\$12{7/52}\$ 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}\$ = \${13 × 37}/{13 + 37}\$ = \${481/50}\$, which is same as: \$9{31/50}\$ m.

### Question 2

What is the length of an edge of a cube if the ratio of volume to the total surface area is 13 : 31?

A

\$2{16/31}\$ units.

B

\$3{19/30}\$ units.

C

\$1{14/33}\$ units.

D

\$5{2/11}\$ 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\$ = \${78/31}\$, which is same as: \$2{16/31}\$.

### Question 3

What is the weight of a hollow cylindrical pipe 14 cm long, and having internal and external radii as 14 and 16 cm? The pipe is made of a metal of density 6 gm/cc. Take π = 22/7.

A

15840 gm.

B

15842 gm.

C

15838 gm.

D

15844 gm.

Soln.
Ans: a

The volume of the pipe is π × (162 - 142) × 14, which is \$22/7\$ × 60 × 14. Weight = vol × density = \$22/7\$ × 60 × 14 × 6 = 15840 gm.

### Question 4

An iron tank 2 m × 6 m is filled with water upto a height of 4 m. What surface area of the tank is at a higher risk of corrosion?

A

76 cu. m.

B

78 cu. m.

C

74 cu. m.

D

80 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 × (6 × 4 + 2 × 4) + 2 × 6. The result is 76 cu. m.

### Question 5

The areas of three adjacent faces of a cube are 5, 6 and 30. It's volume is?

A

30 cu. units.

B

32 cu. units.

C

28 cu. units.

D

34 cu. units.

Soln.
Ans: a

Let the sides be L, B and H. Then LB = 5, BH = 6 and LH = 30. Multiplying all three of them L2B2H2 = (5 × 6 × 30) = 900 = 302, which gives LBH = 30 = volume of the cuboid. 