Chapter 9.2, Problem 35E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

The exhaust chute on a wood chipper has the shape of a frustum of a pyramid. With dimensions as indicated, find the volume (capacity) of the chipper’s exhaust chute.

To determine

**To find:**

The volume (capacity) of the chipper’s exhaust chute.

Explanation

**Given:**

The exhaust chute on a wood chipper 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

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

In a regular pyramid, the lengths of the apothem

**Approach Used:**

i) Calculate the volume of the bigger pyramid

ii) Calculate the volume of the smaller pyramid

iii) Subtract the two to get the volume of the frustum

**Calculation:**

Calculating the volume of the bigger pyramid

with base as a square of side

The area of the square base is

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