Question

Cone A has a radius of 12 inches and Cone B has a radius of 30 inches. If the cones are similar and the volume of Cone A is 48 ft^2, find the volume of Cone B.

Answer 1

750 ft^3

Explanation:

Given that the cones are similar, the first step would be to determine their linear scale factor; That is the ratio of their radii;

`(RadiusB)/(RadiusA)=(30)/(12)=2.5`

The next step is to determine the volume scale factors. Since the linear scale factor is 2.5, the volume scale factor would be;

volume scale factor = (linear scale factor)^3

= 2.5^3 = 125/8

The volume of Cone B will thus be;

volume of Cone A * volume scale factor = 48 * 125/8 = 750 ft^3