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?

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:

Simplifying everything, we obtain

RELATED QUESTIONS
Hello. I was wondering if I could get some assistance on this proof for my geometry... (answered by jim_thompson5910)

If the height of the pyramid is 139 m and the base is a 230 m x 230 m square, what is the (answered by Boreal,ewatrrr)

I DON'T UNDERSTAND PROOFS AT ALL. we're doing them in my geometry class and i'm like.. (answered by elima)

I do not understand proofs at all and I currently have a 60 in my geometry class because... (answered by josgarithmetic)

I need to make a 2 column proof for geometry to prove that, the diagonals of a rectangle... (answered by richwmiller)

Hello First of all in advance I thank you for the help you give me! Okay so here is... (answered by solver91311,MathLover1)

I need you to provide me the Proof of the volume of a sphere, using Geometry, and... (answered by stanbon)

I really need help. I have an awful grade in my geometry class. My chapter test is... (answered by josgarithmetic)

This is a unusual question but I came here because I don’t have anyone else to ask... (answered by MathLover1,ikleyn)