Q36. - Geometry

Question

A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is$\frac{3}{2}{s}^{2}h\sqrt{3}$ .

Step-by-Step Solution

Answer

The volume of the prism is$\frac{3}{2}{s}^{2}h\sqrt{3}$ .

Step 1. Given information.

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

Step 2. Write the concept.

Since base have regular hexagons, then

$B=\frac{3\sqrt{3}}{2}{s}^2$

Step 3. Determine the volume.

Now, the volume of the right prism is:

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

This is the required expression.