Question

A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?

Answer 1

Volume of a sphere, V=4/3πR^3 =972π

Therefore, 4/3R^3=972 =>
`\sqrt[3]{(972*3)/4}` =9 in

Sides of the cube = Radius of sphere*2 = 9*2 = 18 in

Volume of cube = Sides^3 = 18^3 = 5832 in^3

Answer 2

First find the radius of the sphere
V = 4/3 * pi * r^3

Givens
pi but we don't need it's value. We need only know it is on both sides of the equal sign.
V = 972 pi

Formula
V = 4/3 pi r^3

Sub and Solve
972 pi = 4/3 pi r^3 Divide both sides by pi. The 2 pis cancel each other out.
972 = 4/3 R^3 Multiply both sides by 3/4
3/4 * 972= 4/3 * 3/4 * r^3
3/4 * 972 = r^3
729 = r^3
cuberoot(729) = r

Box
r = 9 This is not the answer
d = 2*r
d = 2*9
d = 18

s = d (which is the side of the box
s = 18
V box = 18^3
Vbox = 5832 in^3
Pretty big isn't it?