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Chapter 8: Q. 33 (page 541)

Area of a Segment Find the area of the segment (shaded in blue in the figure) of a circle whose radius is 8 feet, formed by a central angle of 70掳.

[Hint: Subtract the area of the triangle from the area of the sector to obtain the area of the segment.]

Short Answer

Expert verified

The area of the segment is 9.03 square feet.

Step by step solution

01

Step 1. Given information.

The given figure is:

02

Step 2. Determine the area of the sector.

Area of the sector is:

A1=胃360掳脳蟺r2=70掳360掳脳蟺脳(8)2=39.0953...鈮�39.10

03

Step 3. Determine the area of the triangle.

The area of a triangle is:

A2=12absinC=12(8)(8)sin(70掳)=30.0701...鈮�30.07

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=39.10-30.07=9.03

The area of the segment is 9.03 square feet.

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