# Volume and Surface Areas Quiz Set 001

### Question 1

What is the volume of a right cone whose cross-section is an isosceles triangle with base 16 cm and slant height 10 cm?

A

128 π sq. cm.

B

129 π sq. cm.

C

127 π sq. cm.

D

\$43{2/3}\$ π sq. cm.

Soln.
Ans: a

One of the right triangles of the isosceles triangle has its base = 16/2 = 8. By Pythagorean theorem, the height = \$√{10^2 - 8^2}\$ = \$√{100 - 64}\$ = 6. The radius of the base of the cone r = 8 cm, and height h = 6 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(8^2 × 6)\$ = 128π.

### Question 2

What is the volume of a right cone whose cross-section is an isosceles triangle with base 30 cm and height 8 cm?

A

600 π sq. cm.

B

601 π sq. cm.

C

599 π sq. cm.

D

201 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 15 cm, and height h = 8 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(15^2 × 8)\$ = 600π.

### Question 3

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 4

What is the volume of a cone generated by rotating a right angled triangle with sides 17, 15 and 8 cm? The rotation is done about the side of length 8 cm.

A

600 π sq. cm.

B

601 π sq. cm.

C

599 π sq. cm.

D

201 π sq. cm.

Soln.
Ans: a

The radius of the base of the cone r = 15 cm, and height h = 8 cm. The volume is \$1/3\$π\$(r^2 × h)\$ = \$1/3\$π\$(15^2 × 8)\$ = 600π.

### Question 5

What is the volume of rain water collected in a right cylindrical can of radius 8 cm, if 4 cm rainfall is recorded in the city?

A

256 π cu. cm.

B

258 π cu. cm.

C

254 π cu. cm.

D

260 π cu. cm.

Soln.
Ans: a

The height of the can will be filled to 4 cm. The volume of collected water is same as the volume of cylinder with radius 8 cm and height 4 cm., which equals π82 × 4 = 256π cu. cm.