Questions on Geometry: Circles and their properties answered by real tutors!

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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!!: 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(9401) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of the cube:

V=L*W*H Start with the volume equation.


V=4*4*4 Plug in the given dimensions.


V=64 Multiply



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Volume of the sphere:

V=(4/3)pi*r^3


V=(4/3)pi*2^3 Plug in r=2 (note: since the side length is 4, this means that that the diameter is 4)


V=(32/3)pi 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/volume_of_cube=((32/3)pi)/(64)



pi/6 Simplify


So the ratio of the volume of the sphere to the volume of the cube is pi/6


Note: it turns out that the ratio of the volume of the sphere to the volume of the cube is pi/6 no matter what the dimensions of the cube are.



Now approximate pi/6 to get 0.524. So the percentage of the volume of the sphere to the volume of the cube is 52.4%