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Q. 71

Precalculus Mathematics for Calculus
Found in: Page 479
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

Area of a Sector of a Circle Three circles with radii 1, 2, and 3 ft are externally tangent to one another, as shown in the figure. Find the area of the sector of the circle of radius 1 that is cut off by the line segments joining the center of that circle to the centers of the other two circles.

The area of sector is 0.785ft2.

See the step by step solution

Step by Step Solution

Step 1. Given information.

The radius of circle r=1ft

Step 2. Write the concept.

Before applying the formula for area of sector we need to find the central angle theta which the sector subtends.

As, shown in the figure

AB=5ft, BC=3ft and AB=4ft

Applying Pythagoras theorem AC2=AB2+BC2

Also, the area of sector is given by A=12r2θ

Step 3. Determining the values.

Putting the values of Ab, BC and AB in Pythagoras Theorem we find the central angle of the sector as 90.

Therefore the area of sector is:


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