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

Answer:

750 ft^3

Step-by-step 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;

$\frac{RadiusB}{RadiusA}=\frac{30}{12}=2.5$

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