What happens to the volume of a sphere when its diameter is doubled?

Answer 1

When the diameter of a sphere is doubled, its radius also doubles. The volume of a sphere is calculated using the formula ( V = \frac{4}{3} \pi r^3 ). If the radius doubles, the new volume becomes ( V = \frac{4}{3} \pi (2r)^3 = \frac{4}{3} \pi (8r^3) = 8 \times \frac{4}{3} \pi r^3 ). Therefore, the volume of the sphere increases by a factor of eight.