The volume of a sphere is proportional to the cube of its radius:
[tex]V_r=\dfrac{4\pi}3r^3[/tex]
If the radius [tex]r[/tex] is tripled so that the new radius is [tex]R=3r[/tex], then the new volume would be
[tex]V_R=\dfrac{4\pi}3R^3=\dfrac{4\pi}3(3r)^3=\dfrac{4\pi}3(27)r^3=27V_r[/tex]
In other words, an increase in the radius by a factor of 3 results in an increase in volume by a factor of [tex]3^3=27[/tex].
