Question

If the radius of a sphere is tripled, it's volume is multiplied by?.

Answer 1

The volume of a sphere is proportional to the cube of its radius:


`V_r=\frac{4\pi}3r^3`

If the radius
`r` is tripled so that the new radius is
`R=3r`, then the new volume would be


`V_R=\frac{4\pi}3R^3=\frac{4\pi}3(3r)^3=\frac{4\pi}3(27)r^3=27V_r`

In other words, an increase in the radius by a factor of 3 results in an increase in volume by a factor of
`3^3=27`.