Question

Find the volume of the square based pyramid.

Answer 1

Finding the height of the pyramid:

$\left(\dfrac{6}{2} \right )^{\!\!2}+h^{2}=8^{2}\\ \\ \\ 3^{2}+h^{2}=8^{2}\\ \\ h^{2}=8^{2}-3^{2}\\ \\ h^{2}=64-9\\ \\ h^{2}=55\\ \\ h=\sqrt{55}\mathrm{~m}$


Finding the base area:

$S=6^{2}\\ \\ S=36\mathrm{~m^{2}}$


Formula for the volume of the pyramid:

$V=\dfrac{S\cdot h}{3}\\ \\ \\ V=\dfrac{36\cdot \sqrt{55}}{3}\\ \\ \\ V=\dfrac{\diagup\!\!\!\! 3\cdot 12\cdot \sqrt{55}}{\diagup\!\!\!\! 3}\\ \\ \\ \boxed{\begin{array}{c} V=12\sqrt{55}\mathrm{~m^{3}} \end{array}}$

Answer 2

A = 1/3 * s^2 * h where s is a side of the base and h is the height.