Question

If the radius of the smaller sphere is 3 inches and the radius of the larger sphere is 6 inches, how many times greater is the volume of the larger sphere?

(A) 4 times
(B) 6 times
(C) 8 times
(D) 2 times

Answer 1

The volume of the larger sphere is 8 times greater than the volume of the smaller sphere.

Step-by-step explanation:

The volume of a sphere depends on the cube of its radius. Since the radius of the smaller sphere is 3 inches and the radius of the larger sphere is 6 inches, the ratio of their volumes can be calculated by cubing these values.

Volume of smaller sphere = (4/3)π × (3 inches)³

Volume of larger sphere = (4/3)π × (6 inches)³

Dividing the volume of the larger sphere by the volume of the smaller sphere:

(Volume of larger sphere) / (Volume of smaller sphere) = [(4/3)π × (6 inches)³] / [(4/3)π × (3 inches)³] = (6 inches)³ / (3 inches)³ = 6³ / 3³ = 8

Therefore, the volume of the larger sphere is 8 times greater than the volume of the smaller sphere.