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 $40 °$ .

Short Answer

Expert verified

The area of the segment is 0.69 square inches.

Step by step solution

Step 1. Given information.

The radius of the circle is 5 inches.

The central angle is $40 °$ .

Step 2. Determine the area of the sector.

Area of the sector is:

$\begin{array}{rcl} A_{1} & = & \frac{θ}{360 °} \times π r^{2} \\ = & \frac{40 °}{360 °} \times π \times (5)^{2} \\ = & 8.7266 . . . \\ \approx & 8.727 \end{array}$

Step 3. Determine the area of the triangle.

The area of a triangle is:

$\begin{array}{rcl} A_{2} & = & \frac{1}{2} a b \sin C \\ = & \frac{1}{2} (5) (5) \sin (40 °) \\ = & 8.0348 . . . \\ \approx & 8.035 \end{array}$

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.

$\begin{array}{rcl} A & = & A_{1} - A_{2} \\ = & 8.727 - 8.035 \\ = & 0.692 \\ \approx & 0.69 \end{array}$

The area of the segment is 0.69 square inches.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the area of the sector.

Step 3. Determine the area of the triangle.

Step 4. Determine the area of the segment.

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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°.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the area of the sector.

Step 3. Determine the area of the triangle.

Step 4. Determine the area of the segment.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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