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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 9.2, Problem 30E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
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Elementary Geometry for College St...

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.

Chapter 9.2, Problem 30E, Before the shingles of the steeple see Exercise 29 are replaced, an exhaust fan is to be installed

To determine

To find:

The volume of the pyramid.

Explanation

Given:

A regular square pyramid as below,

and lateral edge measures 17ft and each base edge measures 16ft.

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 L of a regular pyramid with slant height of length l and perimeter P of the base is given by

L=12lP.

The total surface area T of a pyramid with lateral area L and base area B is given by

T=L+B.

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

hypotenuse2=base2+perpendicular2.

In a regular pyramid, the lengths of the apothem a of the base, the altitude h, and the slant height l satisfy the Pythagorean Theorem; that is, l2=a2+h2.

The perimeter of the square is four times the side.

The volume V of a pyramid having a base area B and an altitude of length h is given by V=13Bh.

Calculation:

From the given figure

the sides of the square base measure 16ft each and the apothem is half the base length. Hence, a=162=8ft. The lateral edge measures 17ft or e=17ft.

The slant height

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Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E
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