Question

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

Answer 1

Solution

Step 1

$Volume\text{ of a pyramid = }\frac{1}{3}\times\text{ Base area }\times\text{ Height}$

Ste 2:

Use the formula below to find the base area of the regular hexagon

$\begin{gathered} \text{Base area = }\frac{3}{2}\sqrt{3}\text{ s}^2 \\ \text{s = length of base edges = 6 ft} \end{gathered}$

Step 3

$\begin{gathered} Base\text{ area = }\frac{3}{2}\times\sqrt{3}\text{ }\times\text{ 6}^2 \\ \text{= 93.5 ft}^2 \end{gathered}$

Step 4

The height of the pyramid can be found using Pythagorean's Theorem

$\text{Height = }\sqrt{10^2-6^2}\text{ = }\sqrt{100-\text{ 36}}\text{ = }\sqrt{64}\text{ = 8 ft}$

Step 5

The volume is calculated below.

$\begin{gathered} \text{Volume = }\frac{1}{3}\text{ }\times\text{ base area }\times\text{ height} \\ \text{= }\frac{1}{3}\text{ }\times\text{ 93.5 }\times8 \\ \text{= 249.3333333 ft}^3 \end{gathered}$

Final answer

$144\sqrt{3}\text{ or 249.4153163}$