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
