Question

if the radius of the base of a cone is doubled and the height is tripled, find the change in volume​

Answer 1

The new volume in cnange of a cone is 12th times.

Step-by-step explanation:

Let the radius of the base of a cone = r and

The height of the cone = h

To find, the change in volume = ?

We know that,

The volume of a cone = $\dfrac{1}{3} \pi r^2 h$

∴ Rhe radius of the base of new cone = 2r and

The height of the new cone = 3h

∴ The new volume of a cone = $\dfrac{1}{3} \pi (2r)^2 (3h)$

= $\dfrac{1}{3} \pi 4r^2 3h$

$= 12(\dfrac{1}{3} \pi r^2 h)$

The new volume in  cnange of a cone = 12 × The volume of a cone

Thus, the new volume in cnange of a cone is 12th times.