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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8.1, Problem 53E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Area of a Sector of a Circle In Exercises 53 and 54, use the following information. A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure).

Chapter 8.1, Problem 53E, Area of a Sector of a Circle In Exercises 53 and 54, use the following information. A sector of a

For a circle of radius r, the area A of a sector of the circle with central angle θ

(in radians) is given by A = 1 2 r 2 θ .

Sprinkler System A sprinkler in a garden is set to spray water over a distance of 25 feet and rotates through an angle of 120 ° . Find the area of the region.

To determine

To calculate: The area of the region if the water is sprayed from a sprinkler which rotates through an angle of 120°. It sprays water over a distance of 25 ft.

Explanation

Given Information:

The water is sprayed from a sprinkler which rotates through an angle of 120°. It sprays water over a distance of 25 ft. The area of a sector of a circle of radius r and central angle θ is A=12r2θ.

Formula used:

In order to convert the angle from degree to radian, multiply the angle by π radians180°.

Calculation:

Consider the angle of rotation be 120°.

Multiply angle 120° by π radians180° to find the angle in radians.

120°=120°(π radians180°)=2π3radians

The sprinkler sprays water over a distance or radius of r=25 ft

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