Q26. - Geometry

Question

Find the volume of a regular hexagonal pyramid with height 8 cm and base edges 6 cm.

Step-by-Step Solution

Answer

$\text{Volume}=144\sqrt{3}{\text{\hspace{0.17em}\hspace{0.17em}cm}}^3$

Step 1. Given information.

The height of the hexagonal pyramid is equal to8cm and the length of base edge is equal to 6cm.

Step 2. Explanation.

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 side6cm .

$\begin{array}{c}\text{B}=\frac{3\sqrt{3}}{2}{a}^2\\ =\frac{3\sqrt{3}}{2}{\left(6\text{\hspace{0.17em}cm}\right)}^2\\ =\frac{3\sqrt{3}}{2}\left(36{\text{\hspace{0.17em}cm}}^2\right)\\ =54\sqrt{3}{\text{\hspace{0.17em}cm}}^2\end{array}$

Step 3. Determine The volume.

Substitute for B and8 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 height8cm and base edge6cm is equal to$144\sqrt{3}$ .