SOLUTION: Hello, I'm here because I need help doing a proof for my geometry class. I need to prove how the volume of a pyramid is 1/3bh. Is there any way you can help me?
Algebra ->
Geometry-proofs
-> SOLUTION: Hello, I'm here because I need help doing a proof for my geometry class. I need to prove how the volume of a pyramid is 1/3bh. Is there any way you can help me?
Log On
Question 612717: Hello, I'm here because I need help doing a proof for my geometry class. I need to prove how the volume of a pyramid is 1/3bh. Is there any way you can help me? Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! Most of these proofs require a bit of calculus. If we integrate along the height (h), we can say that the volume V is
Here, x is a real number which varies between 0 and h. The (x/h)^2 term "scales" the area of each cross-section of b. As you can see, if x = 0, the cross-sectional area is 0, if x = h, the cross-sectional area is b.
Integrating, we obtain
. We evaluate at x = h, subtract the value obtained at x = 0:
