What happens to the volume of a sphere when the radius is quadrupled?

Answer 1

The volume of a sphere is calculated using the formula ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius. When the radius is quadrupled (i.e., multiplied by 4), the new volume becomes ( V' = \frac{4}{3} \pi (4r)^3 = \frac{4}{3} \pi \cdot 64r^3 = 64 \cdot \frac{4}{3} \pi r^3 ). This means the volume increases by a factor of 64. Therefore, when the radius is quadrupled, the volume of the sphere increases 64 times.