Question

If the height and radius of a cone of volume V are doubled, then the volume of the cone, is

• A. 3V
• B. 4V
• 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

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

if radius and height are doubled,then R=2r and H=2h

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