Question

A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder

Answer 1

Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values. 

Step One
Find the volume of the sphere.

Givens
r = 6 cm

Formula
V = (4/3) pi r^3

Sub and Solve
V =  4/3 pi * 6^3
V = 288 * pi

Step two 
Find the radius of the cylinder

Givens
V = 288* pi cm^3
h = 4.5 cm

Formula
V = pi r^h

Sub and solve
288 pi cm^3 = pi r^2 * 4.5    Divide both sides by pi
288 cm^3 = 4.5 r^2              Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2                                Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer