Q35. - Geometry

Question

A right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is$\frac{1}{4}{x}^3\sqrt{3}$ .

Step-by-Step Solution

Answer

The volume of the prism is$\frac{1}{4}{x}^3\sqrt{3}$ .

Step 1. Given information.

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

Step 2. Write the concept.

Since base have equilateral triangles, then

$B=\frac{\sqrt{3}}{4}{x}^2$

Step 3. Determine the volume.

Now, the volume of the right prism is:

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

This is the required expression.