Question

If the height and radius of a cone of volume $V$ are doubled, then the volume of the cone will be _____.

• A.
  $4V$
• B.
  $3V$
• C.
  $6V$
• D.
  $8V$

Answer 1

The correct option is D

$8V$

Let $r$ and $h$ be the radius and height of a cone, then

$V=\frac{1}{3}\pi r^{2}h$

Let $V^{\prime }$ be the volume of the new cone formed when the radius and height are doubled.

$\Rightarrow V^{\prime }=\frac{1}{3}\pi \left(2r{)}^2\right(2h)=\frac{1}{3}\pi \times 4r^2\times 2h=8\left(\frac{1}{3}\pi r^{2}h\right)=8V$