Chapter 12.1, Problem 35WE

To determine

To show: that the volume of right prism is $\frac{1}{4}{x}^3\sqrt{3}$ .

Explanation of Solution

Given information:

Right prism height is $x$ and base have equilateral triangles with side $x$ .

Calculation: to find the volume of right prism, first find the area of the base,

Since, base have equilateral triangles,

  $B=\frac{\sqrt{3}}{4}{x}^2$

Thus, the volume of the right prism is,

  $\begin{array}{l}v=Bh\\ v=\frac{\sqrt{3}}{4}{x}^2\left(x\right)\text{ [substitute]}\\ v=\frac{1}{4}{x}^3\sqrt{3}\text{ [multiply]}\end{array}$