Chapter 9.2, Problem 30E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Before the shingles of the steeple (see Exercise 29) are replaced, an exhaust fan is to be installed in the steeple. To determine what size exhaust fan should be installed, it is necessary to know the volume of air in the steeple. Find the volume of the regular square pyramid described in Exercise 29.

To determine

**To find:**

The volume of the pyramid.

Explanation

**Given:**

A regular square pyramid as below,

and lateral edge measures

**Properties Used:**

A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.

The lateral area

The total surface area

According to the Pythagorean theorem, in a right-angled triangle

In a regular pyramid, the lengths of the apothem

The perimeter of the square is four times the side.

The volume

**Calculation:**

From the given figure

the sides of the square base measure

The slant height

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