SOLUTION: Can you please explain volumes of pyramids and cones.

Question 592359: Can you please explain volumes of pyramids and cones.
Found 2 solutions by solver91311, richard1234:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Pyramid: One-third of the volume of a prism with the same base area and height.

Cone: One-third of the volume of a cylinder with the same base area and height.

John

My calculator said it, I believe it, that settles it

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Pyramids and cones are quite similar in terms of shape (one could claim that they are "topologically equivalent" -- that is, one could continuously transform the pyramid to obtain the cone, vice versa).

Therefore, their volume formulas are the same. The volume V of a pyramid or cone is equal to

where A is the area of the base and h is the height. This formula is derived using integral calculus; you assume that the pyramid or cone is composed of arbitrarily thin "sheets" stacked on each other, compute the volume of each "sheet" with the height being some infinitely small number (denoted dh), then adding those up via an integral.
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