Answer:
1) ![h=\frac{8\sqrt{3}}{3}\ units](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B3%7D%5C%20units)
2) ![V=\frac{2,048\sqrt{3}}{9}\ units^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%2C048%5Csqrt%7B3%7D%7D%7B9%7D%5C%20units%5E3)
Step-by-step explanation:
Part 1) Find the height of the pyramid
we know that
![tan(30^o)=\frac{h}{(b/2)}](https://tex.z-dn.net/?f=tan%2830%5Eo%29%3D%5Cfrac%7Bh%7D%7B%28b%2F2%29%7D)
where
h is the height of the pyramid
b is the length side of the square base
we have
![tan(30^o)=\frac{\sqrt{3}}{3}](https://tex.z-dn.net/?f=tan%2830%5Eo%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D)
![b=16\ units](https://tex.z-dn.net/?f=b%3D16%5C%20units)
substitute
![\frac{\sqrt{3}}{3}=\frac{h}{(16/2)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D%3D%5Cfrac%7Bh%7D%7B%2816%2F2%29%7D)
![\frac{\sqrt{3}}{3}=\frac{h}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D%3D%5Cfrac%7Bh%7D%7B8%7D)
![h=\frac{8\sqrt{3}}{3}\ units](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B3%7D%5C%20units)
Part 2) Find the volume of the pyramid
we know that
The volume of the pyramid is equal to
![V=\frac{1}{3} Bh](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20Bh)
where
B is the area of the square base
h is the height of the pyramid
we have
![B=(16^2)=256\ units^2](https://tex.z-dn.net/?f=B%3D%2816%5E2%29%3D256%5C%20units%5E2)
![h=\frac{8\sqrt{3}}{3}\ units](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B3%7D%5C%20units)
substitute
![V=\frac{1}{3} (256)(\frac{8\sqrt{3}}{3})](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%28256%29%28%5Cfrac%7B8%5Csqrt%7B3%7D%7D%7B3%7D%29)
![V=\frac{2,048\sqrt{3}}{9}\ units^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%2C048%5Csqrt%7B3%7D%7D%7B9%7D%5C%20units%5E3)