Question

If the radius of the base of a right circular cone is increased by 15%, then the volume of the cone will increase by ______.

• A. 30%
• B. 31%
• C. 32.25%
• D. 34.75%

Answer 1

The correct option is C

32.25%

Let the radius be $x$.

After increase in radius, it would be $1.15x$.

Volume of old cone
$=\frac{1}{3}\pi x^{2}h$

Now, volume of new cone
$=\frac{1}{3}\pi (1.15x{)}^{2}h$

So, increase in volume
= new volume - old volume
$=\frac{1}{3}\pi x^{2}h({1.15}^2-1)$
$=0.3225\times \frac{1}{3}\pi x^{2}h$

Percentage change in volume
$=\frac{IncreaseinVolume}{OldVolume}\times 100\%$

$=\frac{0.3225\times \frac{1}{3}\pi x^{2}h}{\frac{1}{3}\pi x^{2}h}\times 100\%$

$=32.25\%$