Concept explainers
To find: the minimum and maximum volumes of a fire hose in cubic feet.
Answer to Problem 22PPS
The maximum volume is approximately
Explanation of Solution
Given:
The diameters of fire hoses range from 1.5 in. to 6 in.
Thelength of the hoses is 50 ft.
Calculation:
First convert the inches of the diameter into feet. Use the fact that
Convert 1.5 in. into feet.
Next convert 6 in. into feet.
Now, find the volume of the hose having diameter 1.5 in. that is 0.125 ft and the length of the hose 50 ft.
The volume V of the cylinder is given by the formula
where
Since radius is half the diameter of a circle, so radius of the circle is
The area B of the circle is given
Put
Thus, the volume
Therefore, the volume of the hose is
Now, find the volume of the hose having diameter 6 in. that is 0.5 ft and the length of the hose 50 ft.
The volume V of the cylinder is given by the formula
where
Since radius is half the diameter of a circle, so radius of the circle is
The area B of the circle is given
Put
Thus, the volume
Therefore, the volume of the hose is
Conclusion:
Therefore, the maximum volume is approximately
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