Question

Find the height and the volume of a regular hexagonal pyramid with lateral edges 10 ft and base edges 6 ft.

Short answer

The height of the pyramid is8 ft and volume is$144\sqrt{3}{\text{\hspace{0.17em}\hspace{0.17em}ft}}^2$ .

Step-by-step solution

Step 1. Given information.

Base edge of regular hexagonal pyramid is 6 ft and lateral edges are 10 ft.

Step 2. Determine the height.

Use Pythagoras formula,

$\begin{array}{c}h=\sqrt{{\left(10\right)}^2-{\left(6\right)}^2}\\ =\sqrt{100-36}\text{[substitute]}\\ =\sqrt{64}\text{[subtract]}\\ =8\end{array}$

Step 3. Determine the volume.

Now, find the volume of pyramid.

$\begin{array}{c}V=\frac{1}{3}bh\\ =\frac{1}{3}\left(\frac{3\sqrt{3}}{2}{\left(6\right)}^2\right)\left(8\right)\text{[substitute]}\\ =144\sqrt{3}\text{[simplify]}\end{array}$