SOLUTION: A pyramid of volume 344 square units is sliced into two pieces by a plane parallel to the base of the pyramid and 10 units away from the plane of the base. The volume of the result

Question 1137153: A pyramid of volume 344 square units is sliced into two pieces by a plane parallel to the base of the pyramid and 10 units away from the plane of the base. The volume of the resulting frustum is 301 square units. What was the height of the original pyramid?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I will assume you mean to give the volumes in cubic units -- not square units....

The pyramid that was cut off to form the frustum is similar to the original pyramid; the volume of the smaller pyramid is 344-301 = 37 cubic units.

The ratio of the volumes of the small pyramid and the original pyramid is 37:344 = 1:8.

The ratio of volumes of the two similar pyramids is the cube of the ratio of linear measurements of the two pyramids; since 8 = 2^3, the ratio of linear measurements between the two pyramids is 1:2.

That means the height of the pyramid that was cut off is half the height of the original pyramid; that in turn means the height of the frustum is half the height of the original pyramid.

And since the height of the frustum is 10, the height of the original pyramid was 20.
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