# Volume and Surface Areas Quiz Set 020

### Question 1

The areas of three adjacent faces of a cube are 3, 5 and 15. It's volume is?

A

15 cu. units.

B

17 cu. units.

C

13 cu. units.

D

19 cu. units.

Soln.
Ans: a

Let the sides be L, B and H. Then LB = 3, BH = 5 and LH = 15. Multiplying all three of them L2B2H2 = (3 × 5 × 15) = 225 = 152, which gives LBH = 15 = volume of the cuboid.

### Question 2

What is the length of an edge of a cube if the ratio of volume to the total surface area is 7 : 2?

A

21 units.

B

22 units.

C

20 units.

D

8 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\$ = 21.

### Question 3

What is the volume of rain water collected in a right cylindrical can of radius 8 cm, if 5 cm rainfall is recorded in the city?

A

320 π cu. cm.

B

322 π cu. cm.

C

318 π cu. cm.

D

324 π cu. cm.

Soln.
Ans: a

The height of the can will be filled to 5 cm. The volume of collected water is same as the volume of cylinder with radius 8 cm and height 5 cm., which equals π82 × 5 = 320π cu. cm.

### Question 4

What is the volume of a right cone whose cross-section is an isosceles triangle with base 14 cm and slant height 25 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

One of the right triangles of the isosceles triangle has its base = 14/2 = 7. By Pythagorean theorem, the height = \$√{25^2 - 7^2}\$ = \$√{625 - 49}\$ = 24. 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 5

A cone of height 7 cm and radius of base 14 cm is made up of modeling clay. A child reshapes it in the form of a sphere. What is the radius of the sphere?

A

7 cm.

B

9 cm.

C

5 cm.

D

11 cm.

Soln.
Ans: a

Let the radius of the sphere be R. The volumes are equal. So \$4/3\$ π R3 = \$1/3\$ π 142 × 7. Cancelling π/3 from both sides, R3 = \${14 × 14 × 7}/4\$ = 343 = 73. So R = 7 cm.