Question

A cylinder is to be made so that its volume is equal to that of a sphere with a radius of 3 inches. If a cylinder is to have a height of 4 inches, find its radius.

Answer 1

pi(r^2)(h)=4/3(pi)r^3
cylinder=sphere
pi(r^2)(4)=pi(3)^3(4/3)
pi's cancel
r^2(4)=3^2(4)
4's cancel
r^2=3^2
r=3

Answer 2

Vol(sphere) = 4pi/3.r^3 = 4pi/3.3^3 = 36pi [r here is radius of the sphere]
Vol(cylinder) = pi.r^2.h = pi.r^2.4 [r here is the radius of the base of the cylinder]

If Vol(sphere) = Vol(cylinder) then 4pi.r^2 = 36pi => r^2 = 9 and hence r = 3.

Answer 3

Thanks