Chapter 13.5, Problem 14PSC

To determine

To find:The volume of the pyramid.

Answer to Problem 14PSC

The volume of the pyramid is 36

Explanation of Solution

Given:

The base of the triangular pyramid is (6,0,0), (0,6,0) and (0,0,6)

The peak of the pyramid is (0,0,0)

Calculation:

The required diagram is shown below:

  

Calculate the area of the triangle which is considered as the base of the pyramid.

  $\begin{array}{c}{A}_{\Delta }=B_p\\ =\frac{1}{2}\left(6\right)\left(6\right)\\ =18\end{array}$

Calculate the volume of the pyramid.

  $\begin{array}{c}V=\frac{1}{3}{B}_{p}h\\ =\frac{1}{3}\left(18\right)\left(6\right)\\ =36\end{array}$

Thus, the volume of the pyramid is 36