SOLUTION: 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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Question 1189049: 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.
Answer by ikleyn(52803) About Me  (Show Source):
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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 = sqrt%2825%5E2+-+20%5E2-12%5E2%29 = sqrt%2881%29 = 9 cm.


Thus the volume of the parallelepiped is  20*12*9 = 2160 cubic centimeters.    ANSWER

Solved.