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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 9.2, Problem 36E
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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
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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A popcorn container at a movie theatre has the shape of a frustum of a pyramid (see Exercise 35). With dimensions as indicated, find the volume (capacity) of the container.

Chapter 9.2, Problem 36E, A popcorn container at a movie theatre has the shape of a frustum of a pyramid see Exercise 35. With

To determine

To find:

The volume (capacity) of the container.

Explanation

Given:

The popcorn container at a movie theatre is in the shape of a frustum of a pyramid as shown below

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.

A frustum of a pyramid is the portion of a pyramid that lies between its base and a parallel plane that intersects the pyramid.

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.

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.

Approach Used:

i) Calculate the volume of the bigger pyramid VB.

ii) Calculate the volume of the smaller pyramid VS.

iii) Subtract the two to get the volume of the frustum VF=VB−VS.

Calculation:

Calculating the volume of the bigger pyramid

with base as a square of side x=6in and height as h=24in.

The area of the square base is

B=x2=62B=36in2

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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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