   Chapter 9.2, Problem 42E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find the volume of the regular square pyramid that was formed in Exercise 41. To determine

To find:

The volume of the regular square pyramid.

Explanation

Given:

The four congruent isosceles triangles are folded upward it forms a regular square pyramid and the figure given below

From question 41, the slant height is 5" and base area is B=36in2.

Properties Used:

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

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

hypotenuse2=base2+perpendicular2.

The area of the square is side2.

Approach Used:

i) Calculate the apothem of a square base a=side2.

ii) Using the property l2=a2+h2, find the height or altitude h by substituting the values of l and a.

iii) Calculate the base area B of the square base formed.

iv) Substitute the values of area B and the height h in equation V=13Bh to find the value of volume V.

Calculation:

From the figure below,

considering one of the lateral faces which is an isosceles triangle

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