Question

The volume of a right circular cone is 15 π feet. the radius of the cone is tripled and its height does not change. by what factor is the volume of the first cone multiplied?

Answer 1

The volume of the first cone is multiplied by a factor of 27.

Step-by-step explanation:

To find the factor by which the volume of the first cone is multiplied, we need to calculate the volume of the new cone. The formula for the volume of a cone is V = 1/3 * π * r^2 * h. Since the height does not change, we only need to consider the change in the radius.

Let's denote the original radius as 'r' and the new radius as '3r'. Since the volume is proportional to the cube of the radius, the factor by which the volume is multiplied is (3r)^3 / r^3 = 27.