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?
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?
