Question

Find the volume of the square based pyramid.

Answer 1

Finding the height of the pyramid:


`\left((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=√(55)\mathrm{~m}`


Finding the base area:


`S=6^(2)\\ \\ S=36\mathrm{~m^(2)}`


Formula for the volume of the pyramid:


`V=(S\cdot h)/(3)\\ \\ \\ V=(36\cdot √(55))/(3)\\ \\ \\ V=(\diagup\!\!\!\! 3\cdot 12\cdot √(55))/(\diagup\!\!\!\! 3)\\ \\ \\ \boxed{\begin{array}{c} V=12√(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.