# Volume and Surface Areas Quiz Set 019

### Question 1

What is the surface area of the cuboid obtained by joining two equal cubes of 512 cu. cm volume each?

A

640 sq. cm.

B

642 sq. cm.

C

638 sq. cm.

D

644 sq. cm.

Soln.
Ans: a

Let the side of a cube be L. Then L3 = 512, which gives L = 8. The resulting cuboid has L = L, H = L, and B = 2L. The surface area is 2 × (LB + BH + HL) = 2 × (2L2 + 2L2 + L2) = 10 × L2 = 10 × 82 = 640 sq. cm.

### Question 2

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 3

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 4

How much water flows per hour through a pipe of radius 2 cm, if water flows at 10 km/h?

A

4 π cu. m.

B

6 π cu. m.

C

10 π cu. m.

D

8 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 × \${2 × 2 × 10 × 1000}/{100 × 100}\$, which can easily be cancelled to get 4π cu. m.

### Question 5

What is the surface area of the cuboid obtained by joining two equal cubes of 343 cu. cm volume each?

A

490 sq. cm.

B

492 sq. cm.

C

488 sq. cm.

D

494 sq. cm.

Soln.
Ans: a

Let the side of a cube be L. Then L3 = 343, which gives L = 7. The resulting cuboid has L = L, H = L, and B = 2L. The surface area is 2 × (LB + BH + HL) = 2 × (2L2 + 2L2 + L2) = 10 × L2 = 10 × 72 = 490 sq. cm. 