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!!

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) (Show Source): You can put this solution on YOUR website!
Volume of the cube:

Start with the volume equation.

Plug in the given dimensions.

Multiply

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

Volume of the sphere:

Plug in (note: since the side length is 4, this means that that the diameter is 4)

Evaluate the right side.

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

Simplify

So the ratio of the volume of the sphere to the volume of the cube is

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

Now approximate to get . So the percentage of the volume of the sphere to the volume of the cube is 52.4%

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