Chapter 12: Q36. (page 480)

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

Short Answer

Expert verified

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

Step by step solution

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:

$\begin{matrix} v = B h \\ = \frac{3 \sqrt{3}}{2} s^{2} (h) [substitute] \\ = \frac{3}{2} s^{2} h \sqrt{3} [multiply] \end{matrix}$

This is the required expression.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the volume.

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A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is32s2h3.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the volume.

One App. One Place for Learning.

Most popular questions from this chapter

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Mechanics Maths

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