SOLUTION: A rectangular prism has a height of 12 cm and a square base with sides measuring 5 cm. A pyramid with the same base and the height of the prism is placed inside the prism. What i

Algebra ->  Volume -> SOLUTION: A rectangular prism has a height of 12 cm and a square base with sides measuring 5 cm. A pyramid with the same base and the height of the prism is placed inside the prism. What i      Log On


   

Question 876425: A rectangular prism has a height of 12 cm and a square base with sides measuring 5 cm. A pyramid with the same base and the height of the prism is placed inside the prism. What is the volume of the space outside the pyramid but inside the prism
Answer by KMST(5328) About Me  (Show Source):
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The volume of a rectangular prism is (area of base)(height) .
The base of the prism is a square with sides measuring 5 cm, so its area is
%285cm%29%285cm%29=25squarecm .
So the volume of the prism, in cubic cm, is
25%2A12=300 .

The volume of a pyramid is (1/3)(area of base)(height) .
It is 1%2F3 of the volume of a rectangular prism with the same base and height.
So the volume of the pyramid in this problem, in cubic cm, is
%281%2F3%29%28300%29=100 .
So the volume of the space outside the pyramid but inside the prism, in cubic cm, is
300-100=highlight%28200%29 .