SOLUTION: Four identical pieces are cut off the sides of a cylinder, as shown. The remaining shape is a square prism. The diagonal of the prism's square base is as long as the diameter of th

Algebra ->  Pythagorean-theorem -> SOLUTION: Four identical pieces are cut off the sides of a cylinder, as shown. The remaining shape is a square prism. The diagonal of the prism's square base is as long as the diameter of th      Log On


   

Question 1134728: Four identical pieces are cut off the sides of a cylinder, as shown. The remaining shape is a square prism. The diagonal of the prism's square base is as long as the diameter of the cylinder. The diameter of the cylinder was 12 centimeters, and the height of the cylinder was 4.6 centimeters. Find the exact length of a side of the square base of the prism. Then find an approximate volume of the prism.
Answer by greenestamps(13200) About Me  (Show Source):
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Diameter of cylinder = diagonal of base of square prism = 12cm, so the side of the base of the square prism is 12/sqrt(2) cm = 6*sqrt(2) cm.

The volume of the square prism is base times height = (6*sqrt(2))^2 times 4.6 = 72*4.6 = 331.2 cm^3