Question

A cylindrical rod with radius of 2 inches and height of 5 inches was melted. This melted liquid was used to make some solid cones of radius of 1 inch and height of 2 inches. How many such cones can be made?

• A. 15
• B. 39
• C. 30
• D. 24

Answer 1

The correct option is C 30

For the cylindrical rod:
Radius = 2 in
Height = 5 in
Therefore, volume $=\pi r^{2}h$
$=\pi \times 2^2\times 5\text{cu in}$
$=\pi \times 4\times 5\text{cu in}$
$=20\pi \text{cu in}$

For the solid cones:
Radius = 1 in
Height = 2 in

Therefore, volume of the cones
$=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi 1^2\times 2\text{cu in}$
$=\frac{2\pi }{3}\text{cu in}$

Volume of cylinder
= Sum of volumes of cones formed

Hence, the number of the solid cones
$=\frac{\text{Volume of the cylindrical rod}}{\text{Volume of the solid cones}}$
$=\frac{20\pi }{\frac{2\pi }{3}}$
$=\frac{20\times 3}{2}$
$=10\times 3=30$