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A rectangular parallelepiped is inscribed in a sphere whose diameter is 25 cm.
find the volume of the parallelepiped if its length is 20 cm and its width is 12 cm.
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Notice that the longest 3D diagonal of the parallelepiped is the diameter of the sphere.
So, apply the 3D Pythagorean formula
25^2 = 20^2 + 12^2 + h^2
where h is the height of the parallelepiped, which is the only unknown its dimension.
From the equation, h = = = 9 cm.
Thus the volume of the parallelepiped is 20*12*9 = 2160 cubic centimeters. ANSWER
Solved.