Chapter 12.1, Problem 36WE

To determine

To show: that the volume of right prism is $\frac{3}{2}{s}^{2}h\sqrt{3}$ .

Explanation of Solution

Given information:

Right prism height is $h$ and base have regular hexagons with side $s$ .

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

Since, base have regular hexagons,

  $B=\frac{3\sqrt{3}}{2}{s}^2$

Thus, the volume of the right prism is,

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