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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 12: Q18. (page 485)

Find the height and the volume of a regular hexagonal pyramid with lateral edges 10 ft and base edges 6 ft.

Short Answer

Expert verified

The height of the pyramid is8 ft and volume is $144 \sqrt{3} {ft}^{2}$ .

Step by step solution

01

Step 1. Given information.

Base edge of regular hexagonal pyramid is 6 ft and lateral edges are 10 ft.

02

Step 2. Determine the height.

Use Pythagoras formula,

$\begin{matrix} h = \sqrt{{(10)}^{2} - {(6)}^{2}} \\ = \sqrt{100 - 36} [substitute] \\ = \sqrt{64} [subtract] \\ = 8 \end{matrix}$

03

Step 3. Determine the volume.

Now, find the volume of pyramid.

$\begin{matrix} V = \frac{1}{3} b h \\ = \frac{1}{3} (\frac{3 \sqrt{3}}{2} {(6)}^{2}) (8) [substitute] \\ = 144 \sqrt{3} [simplify] \end{matrix}$

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Most popular questions from this chapter

Copy and complete the table below for the regular square pyramid.

$\begin{matrix} Height, h \\ Slant Height, l & 12 \\ Base edge \\ Lateral edge & 15 \end{matrix}$

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Refer to cubes with edges of length e. Complete the following table.

$\begin{matrix} e & 2 x \\ T . A . \\ V \end{matrix}$

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