SOLUTION: Sarah buys her friend, Alyssa, a birthday present. She decides to mail her a bowling ball. The bowling ball fits tightly into a box that is a cube. Sarah would like to fill the ext

Algebra ->  Formulas -> SOLUTION: Sarah buys her friend, Alyssa, a birthday present. She decides to mail her a bowling ball. The bowling ball fits tightly into a box that is a cube. Sarah would like to fill the ext      Log On


   

Question 831365: Sarah buys her friend, Alyssa, a birthday present. She decides to mail her a bowling ball. The bowling ball fits tightly into a box that is a cube. Sarah would like to fill the extra space in the box with foam packing material.
What percent of the volume (space) of the box that remains and needs to be filled with the packing material?
*I don't know how to start this problem. The problem doesn't state the radius or diameter. Any help is greatly appreciated*
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The bowling ball fits tightly into a box that is a cube.
Sarah would like to fill the extra space in the box with foam packing material.
What percent of the volume (space) of the box that remains and needs to be filled with the packing material?
:
Let s = the side of the box
then
s^3 = the volume of the box
:
Since the ball fits tightly we can say the length of the side = diameter of the ball
radius = .5s
4%2F3pi%2A%28.5s%29%5E3 = the volume of the ball
4%2F3pi%2A.125s%5E3 = the volume of the ball
We can write it
pi%2A.167s%5E3
:
the volume of the packing material = vol of the box - vol of the ball
Then the percent packing material would be
%28s%5E3-%28pi%2A.167s%5E3%29%29%2Fs%5E3 * 100 =
Cancel out s^3 mult by 100
1+-+%28.3167%2Api%29 * 100 = 47.6% packing material