   Chapter 9.1, Problem 30E 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

A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases. With dimensions as shown, what is the storage capacity (volume) of its interior? To determine

To find:

The storage capacity (volume) of the interior of the storage shed in the shape of a trapezoidal prism.

Explanation

The volume of any solid is the region of space occupied by it and in general the volume of a solid is given by the product of its base area and altitude.

For a regular solid prism with base area B and altitude h, the volume is given by the formula

V=Bh.

Calculation:

Given,

The volume of the a prism with base area ‘B’ and height ‘h’ is given by the formula.

V=Bh

First let us calculate the base area of the prism.

The base of the prism is trapezoidal and its area is given by the formula.

B=12h(a+b)

Here, ‘a’ and ‘b’ are the length of the parallel sides of the trapezium and ‘h’ is the altitude of the trapezium.

From the given figure we have,

a=8 in

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