Irrigation An irrigation system uses a straight sprinkler pipe 300 ft long that pivots around a central point as shown. Because of an obstacle the pipe is allowed to pivot through 280° only. Find the area irrigated by this system.
The area of the irrigated part from the sprinkler pipe.
Answer to Problem 76E
Area of the irrigated part from the sprinkler pipe is
Explanation of Solution
Given:
Length of the sprinkler pipe is
The angle is
Formulas used:
Area of the circular sector is,
Area of a circle is,
Conversion of degree to radian is
Calculation:
The sprinkler pipe makes a circular path covering the irrigated portion.
Therefore the area is taken as a circle of angle
Angle for the sector is,
Convert
Substitute
Area of the circular sector is
Substitute
The area of circle is
For calculating the area of irrigated portion, subtract area of sector from the area of the circle.
Substitute
Thus the area of the irrigated part from the sprinkler pipe is
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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