   Chapter 9.1, Problem 43E 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

For Exercise 41 to 44, 1 f t 3 of liquid corresponds to 7.5 gallons of the liquid.The playing surface of football field is 160 feet by 300 feet. To improve drainage, Rhydian(the groundskeeper) contemplates the potential of a 1 in. downpour.a) How many cubic feet of rain would cover the field during the 1 in. downpour?b) How many gallons of rainfall are represented by the answer in part(a)?

To determine

a)

The quantity of the rain that would cover the Field.

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,

Dimension of a Football Field is 160 feet by 300 feet.

Downpour of the rainwater = 1in.

The dimensions of the rainwater that covers the Field is given by

l=160 feet,

w=300 feet, and

h=1 in.

of the above three given measures height of the box is measured by the unit of inches while the other two are measured by the unit of foot.

Thus, it is necessary to convert the measure of height from the unit of inches to Foot, for the units need to be uniform.

1 foot=12 inches.

112 foot=1 inch

To determine

b)

The quantity of rainfall in gallons.

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