SOLUTION: A squash ball fits snugly inside a cubical box whose edges are 4 cm long. Find the percentage of the box's volume that the ball occupies. thank you!!

Algebra ->  Circles -> SOLUTION: A squash ball fits snugly inside a cubical box whose edges are 4 cm long. Find the percentage of the box's volume that the ball occupies. thank you!!      Log On


   

Question 149466: A squash ball fits snugly inside a cubical box whose edges are 4 cm long.
Find the percentage of the box's volume that the ball occupies.


thank you!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of the cube:

V=L%2AW%2AH Start with the volume equation.


V=4%2A4%2A4 Plug in the given dimensions.


V=64 Multiply



--------------

Volume of the sphere:

V=%284%2F3%29pi%2Ar%5E3


V=%284%2F3%29pi%2A2%5E3 Plug in r=2 (note: since the side length is 4, this means that that the diameter is 4)


V=%2832%2F3%29pi Evaluate the right side.




So to find the percentage, simply divide the volume of the sphere by the volume of the cube


volume_of_sphere%2Fvolume_of_cube=%28%2832%2F3%29pi%29%2F%2864%29



pi%2F6 Simplify


So the ratio of the volume of the sphere to the volume of the cube is pi%2F6


Note: it turns out that the ratio of the volume of the sphere to the volume of the cube is pi%2F6 no matter what the dimensions of the cube are.



Now approximate pi%2F6 to get 0.524. So the percentage of the volume of the sphere to the volume of the cube is 52.4%