Height & volume of pyramid?? Please help.

[Guest]

9) The volume of a pyramid with a square base is given by the formula , where L = length of the side of the base and H = height of the pyramid.

a) Solve the formula for height, H.


b) Use the new version of the formula to find the height if the volume of the pyramid is 144 cubic meters and its base length is 12 meters.

[Guest]

The volume [tex]V[/tex] is given by
[tex]V=\frac{L^2 H}{3}[/tex]
https://en.wikipedia.org/wiki/Square_py ... e_pyramids

To solve for [tex]H[/tex], we need to do identical operations on both sides of the equal sign that eventually leaves [tex]H[/tex] only on one side.
[tex]V=\frac{L^2 H}{3}\quad[/tex] (Starting formula. First we'll try and get rid of 3 on the right hand side.)
[tex]3V = \frac{3 L^2 H}{3}\quad[/tex] (Multiply both sides by 3)
[tex]3V = L^2 H\quad[/tex] (The two 3s on the right hand side cancel each other out. Next we'll try and get rid of the [tex]L^2[/tex].)
[tex]\frac{3V}{L^2} = \frac{L^2 H}{L^2}\quad[/tex] (Divide both sides by [tex]L^2[/tex])
[tex]\frac{3V}{L^2} = H\quad[/tex] (The two [tex]L^2[/tex] terms on the right hand side cancel each other out)

So [tex]H = \frac{3V}{L^2}[/tex].

For part (b) substitute [tex]V=144[/tex] and [tex]L=12[/tex] into the above formula to get [tex]H=3[/tex] meters.

Hope this helped,

R. Baber.