SOLUTION: A right pyramid has a volume of 200 cubic centimeter and an altitude of 20 cm. How far from the vertex must it be cut so that the two solids cut have equal volume?
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Question 1116877: A right pyramid has a volume of 200 cubic centimeter and an altitude of 20 cm. How far from the vertex must it be cut so that the two solids cut have equal volume? Answer by greenestamps(13200) (Show Source):
The pyramid is cut into a smaller, similar pyramid and a frustum.
Since the two pieces have the same volume, the volume of the small pyramid is 1/2 the volume of the original pyramid.
Since the two pyramids are similar, the ratio of volumes is the cube of the ratio of linear measurements. Since the altitude of the original pyramid is 20cm, the altitude of the small pyramid, to a few decimal places in cm, is .
The altitude of the small pyramid is the distance from the vertex at which the original pyramid must be cut, so the answer to the problem is 15.874 cm.
