Question

The height and base radius of a cone are each increased by $100\%$, then the volume of the cone becomes:

• A. double
• B. three times
• C. six times
• D. eight times

Answer 1

The correct option is D eight times

Let the radius and height of the cone be $R$ and $H$ then

$V_1=\frac{1}{3}\times \pi \times (R{)}^2\times (H)$

When radius and height are increased by $100\%$ each then

$V_2=\frac{1}{3}\times \pi \times (2R{)}^2\times (2H)$

$V_2=8\times \frac{1}{3}\times \pi \times (R{)}^2\times (H)$

Hence,

$V_2=8\times \left(V_1\right)$

So, the volume becomes eight times when radius and height are doubled.