Chapter 12.2, Problem 26WE

To determine

To find: The volume of the hexagonal pyramid with height $8\text{cm}$ and base edge $6\text{cm}$ .

Answer to Problem 26WE

The volume of the hexagonal pyramid with height $8\text{cm}$ and base edge $6\text{cm}$ is equal to $144\sqrt{3}$ .

Explanation of Solution

Given information:

The height of the hexagonal pyramid is equal to $8\text{cm}$ and the length of base edge is equal to $6\text{cm}$ .

Calculation:

The formula for the volume of pyramid is the one third of the product of base area and height.

  $\text{V}=\frac{1}{3}\text{B}h$

Simplify the base area of hexagonal triangle with side $6\text{cm}$ .

  $\begin{array}{c}\text{B}=\frac{3\sqrt{3}}{2}{a}^2\\ =\frac{3\sqrt{3}}{2}{\left(6\text{cm}\right)}^2\\ =\frac{3\sqrt{3}}{2}\left(36{\text{cm}}^2\right)\\ =54\sqrt{3}{\text{cm}}^2\end{array}$

Substitute $54\sqrt{3}$ for $\text{B}$ and $8$ for $h$ in the formula for volume of pyramid.

  $\begin{array}{c}\text{V}=\frac{1}{3}\text{B}h\\ =\frac{1}{3}\left(54\sqrt{3}\right)\left(8\right)\\ =18\sqrt{3}\times 8\\ =144\sqrt{3}\end{array}$

Therefore, the volume of the hexagonal pyramid with height $8\text{cm}$ and base edge $6\text{cm}$ is equal to $144\sqrt{3}$ .