Question

The material of a solid cone is converted into the shape of a solid cylinder of equal radius. If the height of the cylinder is $5$ cm, what is the height of the cone?

• A. $15$ cm
• B. $20$ cm
• C. $25$ cm
• D. $30$ cm

Answer 1

The correct option is A $15$ cm

Given that solid cone is converted into shape of solid cylinder of equal radius.

Then their volumes must be equal.

Therefore, volume of cone $=$ volume of cylinder

Here height of cylinder is $5$ cm. We need to find height of cone.

Let height of cone be $h$ and height of cylinder be $H$.

Thus $\frac{1}{3}\pi .r^2.h=\pi r^{2}H$

$\Rightarrow \frac{1}{3}\pi r^{2}h=5.\pi r^2$
$\Rightarrow h=15$ cm