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Chapter 8: Q. 34 (page 541)

Area of a Segment Find the area of the segment of a circle whose radius is 5 inches, formed by a central angle of 40掳.

Short Answer

Expert verified

The area of the segment is 0.69 square inches.

Step by step solution

01

Step 1. Given information.

The radius of the circle is 5 inches.

The central angle is 40掳.

02

Step 2. Determine the area of the sector.

Area of the sector is:

A1=胃360掳脳蟺r2=40掳360掳脳蟺脳(5)2=8.7266...鈮�8.727

03

Step 3. Determine the area of the triangle.

The area of a triangle is:

A2=12absinC=12(5)(5)sin(40掳)=8.0348...鈮�8.035

04

Step 4. Determine the area of the segment.

Subtract the area of the triangle from the area of the sector to obtain the area of the segment.

A=A1-A2=8.727-8.035=0.692鈮�0.69

The area of the segment is 0.69 square inches.

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