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Home Q & A Board Science-Related Homework Help Mathematics
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hurenhuo hurenhuo
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11 years ago
Pass a plane containing a vertex of a rectangular parallelepiped and a diagonal of a face not containing that vertex to cut a pyramid from the paralellepiped. What fraction of the volume of the parallelepiped is the volume of the pyramid thus cut off?
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#1
11 years ago
The answer is again 1/6 (see my answer to your previous question).
Taking as a base the triangle, whose side is the face diagonal, its area is 1/2 of the area of a rectangular face (every diagonal divides a parallelogram into 2 congruent triangles), the altitude of the pyramid will be the edge through the given vertex, perpendicular to the base. Now the desired result follows from the formula for the volume of a pyramid.
By the way the answer is the same if the parallelepiped is not necessarily rectangular.
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