Given two spheres, if the volume of the first sphere is 36r, and the volume of the second sphere is 288r, what is the relation of the second radius to the first radius?

Answer 1

V1 = (4pi/3)r^3 = 36r,
Divide both sides by r:
(4pi/3)r^2 = 36,
Multiply both sides by 3/4pi:
r^2 = 36 * 3/4pi,
r^2 = 27/pi = 8.59,
r = 2.93.

V2 = (4pi/3)r^3 = 288r,
(4pi/3)r^2 = 288,
r^2 = 288(3/4pi) = 216/pi = 68.75,
r = 8.29.

r2/r1 = 8.29/2.93 = 2.83,
r2 = 2.83r1.