# Thread: Volume of a pyramid

1. ## Volume of a pyramid

--> Volume = $\displaystyle \lim \Delta y \rightarrow \infty \sum s^2 \Delta y$

How do you proceed from there?

2. If s is the length of a side of the slice and h is the height of the pyramid, then by similar triangles:

$\displaystyle \frac{\frac{1}{2}s}{\frac{1}{2}a}=\frac{h-y}{h}$

or $\displaystyle s=\frac{a}{h}(h-y)$

The area, A(y), of the cross section at y is:

$\displaystyle A(y)=s^{2}=\frac{a^{2}}{h^{2}}(h-y)^{2}$

Therefore, the volume is:

$\displaystyle \int_{0}^{h}A(y)dy=\frac{a^{2}}{h^{2}}\int_{0}^{h} (h-y)^{2}dy$

Using a=2, perform the integration and you should get $\displaystyle \frac{1}{3}(2)^{2}h$

3. I got 8/3
I did every thing correct though