# Volume and Surface Areas Quiz Set 007

### Question 1

What is the surface area of the cuboid obtained by joining two equal cubes of 216 cu. cm volume each?

A

360 sq. cm.

B

362 sq. cm.

C

358 sq. cm.

D

364 sq. cm.

Soln.
Ans: a

Let the side of a cube be L. Then L3 = 216, which gives L = 6. 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 × 62 = 360 sq. cm.

### Question 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 24 cm and slant height 20 cm?

A

768 π sq. cm.

B

769 π sq. cm.

C

767 π sq. cm.

D

257 π sq. cm.

Soln.
Ans: a

One of the right triangles of the isosceles triangle has its base = 24/2 = 12. By Pythagorean theorem, the height = $√{20^2 - 12^2}$ = $√{400 - 144}$ = 16. The radius of the base of the cone r = 12 cm, and height h = 16 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(12^2 × 16)$ = 768π.

### Question 3

A cone of height 2 cm and radius of base 4 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

2 cm.

B

4 cm.

C

8 cm.

D

6 cm.

Soln.
Ans: a

Let the radius of the sphere be R. The volumes are equal. So $4/3$ π R3 = $1/3$ π 42 × 2. Cancelling π/3 from both sides, R3 = ${4 × 4 × 2}/4$ = 8 = 23. So R = 2 cm.

### Question 4

What is the radius of a sphere if the ratio of volume to the surface area is 23 : 19?

A

$3{12/19}$ units.

B

$4{8/9}$ units.

C

$2{8/21}$ units.

D

6 units.

Soln.
Ans: a

Let R be the radius. Then $V/S = {4/3 × \text"π" × R^3}/{4 × \text"π" × R^2}$ = $R/3$, so R = 3 × ratio = ${69/19}$, which is same as: $3{12/19}$.

### Question 5

What is the volume of a right cone whose cross-section is an isosceles triangle with base 18 cm and slant height 41 cm?

A

1080 π sq. cm.

B

1081 π sq. cm.

C

1079 π sq. cm.

D

361 π sq. cm.

Soln.
Ans: a

One of the right triangles of the isosceles triangle has its base = 18/2 = 9. By Pythagorean theorem, the height = $√{41^2 - 9^2}$ = $√{1681 - 81}$ = 40. The radius of the base of the cone r = 9 cm, and height h = 40 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(9^2 × 40)$ = 1080π. 