Exact Volume = 12348pi
Approximate Volume = 38772.72 (when using pi = 3.14)
Units for the volume are in cubic inches
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Explanation:
The cube has a side length of 42 inches.
Because the sphere is as large as possible, yet fully contained in the box, this means the diameter of the sphere is 42 inches.
If the diameter is 42, then the radius is half that at 21.
Plug r = 21 into the formula below to compute the volume of the sphere
V = (4/3)*pi*r^3
V = (4/3)*pi*21^3
V = (4/3)*21^3*pi
V = 12348pi .... exact volume
If we use the approximation pi = 3.14, then we would get,
V = 12348*pi
V = 12348*3.14
V = 38772.72 .... approximate volume
The units for the volume are in cubic inches. If you need more accuracy for the approximate volume, then use more decimal digits of pi.
