Chapter 12, Problem 5CR

To determine

To find: The volume of a regular triangular pyramid.

Answer to Problem 5CR

The volume of a regular triangular pyramid is $\frac{160\sqrt{3}}{3}$ cubic units.

Explanation of Solution

Given information:

The base edge of regular triangular pyramid is 8 and the height is 10.

Calculation:

The base of regular pyramid is an equilateral triangle. Length of base edge is 8.

The formula to find base area of aregular triangular pyramid is:

  $\text{Base}\text{area}=\frac{\sqrt{3}}{4}\times {\left(\text{side}\right)}^2$

Substitute 8 for side in above formula.

  $\begin{array}{c}\text{Base}\text{area}=\frac{\sqrt{3}}{4}\times {\left(8\right)}^2\\ =\frac{\sqrt{3}}{4}\times 64\\ =16\sqrt{3}\end{array}$

The formula for the volume of a triangular pyramid is:

  $V=\frac{1}{3}\times \text{base}\text{area}\times \text{height}$

Substitute 10 for height in above formula.

  $\begin{array}{c}V=\frac{1}{3}\times 16\sqrt{3}\times 10\\ =\frac{160\sqrt{3}}{3}\end{array}$

Therefore, the volume of a regular triangular pyramid is $\frac{160\sqrt{3}}{3}$ cubic units.