When the radius doubles what happens to the volume of a figure?

Answer 1

When the radius of a spherical figure doubles, its volume increases by a factor of eight. This is because the volume ( V ) of a sphere is calculated using the formula ( V = \frac{4}{3} \pi r^3 ). When the radius ( r ) is doubled (to ( 2r )), 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 ), resulting in eight times the original volume.