Question

A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by $$A=\frac{1}{2} r^{2} \theta$$ (GRAPH CAN'T COPY). where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians. In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle. $r=120$ centimeters, $\theta=0.65$ radian

Name: Problem 89, Chapter 4: Essentials of Precalculus
Uploaded: 2021-07-11T00:51:00-08:00
Duration: 38 s
Channel: Erika Bustos

   A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by
$$A=\frac{1}{2} r^{2} \theta$$
(GRAPH CAN'T COPY).
where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians.
In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle.
$r=120$ centimeters, $\theta=0.65$ radian

Essentials of Precalculus

Richard N. Aufmann,… 1st Edition

Chapter 4, Problem 89

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Solved by Expert Erika Bustos

07/11/2021

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65$ radians. We are asked to find the area of the sector. Show more…

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A sector of a circle is the region bounded by radii OA and OB and the intercepted arc $A B$. See the following figure. The area of the sector is given by $$A=\frac{1}{2} r^{2} \theta$$ (GRAPH CAN'T COPY). where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians. In Exercises 87 to $90,$ find the area, to the nearest square unit, of the sector of a circle with the given radius and central angle. $r=120$ centimeters, $\theta=0.65$ radian

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Key Concepts

Sector of a Circle

A sector is a portion of a circle bounded by two radii and the arc between them. Understanding sectors is essential in geometry to analyze parts of circular figures, especially when dealing with areas and angles.

Radian Measure

Radians are an alternative to degrees for measuring angles, where one radian is defined by the angle created when the arc length equals the radius of the circle. This measurement simplifies many mathematical formulas involving circles because it provides a direct relationship between the angle and the corresponding arc length.

Area Formula for a Sector

The area of a sector of a circle is calculated using the formula A = 1/2 r²?, where r is the radius and ? is the central angle measured in radians. This formula is derived by relating the area of the sector to the area of the entire circle, with the fraction of the circle represented by the ratio of the angle to the full angle in radians (2?).

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