# Volume and Surface Areas Quiz Set 003

### Question 1

The slant height of a right conical tent of height 21 m is 29 m. What is the curved surface area?

A

580 π sq. m.

B

581 π sq. m.

C

579 π sq. m.

D

582 π sq. m.

Soln.
Ans: a

By Pythagorean theorem, the radius of base = \$√{29^2 - 21^2}\$ = \$√{841 - 441}\$ = 20. The volume is π × r × l = π × 20 × 29 = 580π sq. m.

### Question 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 6 cm and height 4 cm?

A

12 π sq. cm.

B

13 π sq. cm.

C

11 π sq. cm.

D

5 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 3 cm, and height h = 4 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(3^2 × 4)\$ = 12π.

### Question 3

What is the volume of a cone generated by rotating a right angled triangle with sides 29, 21 and 20 cm? The rotation is done about the side of length 20 cm.

A

2940 π sq. cm.

B

2941 π sq. cm.

C

2939 π sq. cm.

D

981 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 21 cm, and height h = 20 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(21^2 × 20)\$ = 2940π.

### Question 4

How much water flows per hour through a pipe of radius 17 cm, if water flows at 10 km/h?

A

289 π cu. m.

B

291 π cu. m.

C

287 π cu. m.

D

293 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 × \${17 × 17 × 10 × 1000}/{100 × 100}\$, which can easily be cancelled to get 289π cu. m.

### Question 5

What is the surface area of the cuboid obtained by joining two equal cubes of 64 cu. cm volume each?

A

160 sq. cm.

B

162 sq. cm.

C

158 sq. cm.

D

164 sq. cm.

Soln.
Ans: a

Let the side of a cube be L. Then L3 = 64, which gives L = 4. 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 × 42 = 160 sq. cm. 