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. $$r=2.8 \text { feet, } \theta=\frac{5 \pi}{2} \text { radians }$$

Name: Problem 88, Chapter 4: Essentials of Precalculus
Uploaded: 2021-07-11T00:52:05-08:00
Duration: 37 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.
$$r=2.8 \text { feet, } \theta=\frac{5 \pi}{2} \text { radians }$$

Essentials of Precalculus

Richard N. Aufmann,… 1st Edition

Chapter 4, Problem 88

Instant Answer

Solved by Expert Erika Bustos

07/11/2021

Step 1

Step 1: First, we need to use the formula for the area of a sector of a circle, which is given by $$A=\frac{1}{2} r^{2} \theta$$ where $r$ is the radius of the circle and $\theta$ is the measure of the central angle in radians. 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. $$r=2.8 \text { feet, } \theta=\frac{5 \pi}{2} \text { radians }$$

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Key Concepts

Sector of a Circle

A sector is a portion of a circle which is bounded by two radii and the arc between them. It represents a 'slice' of the circle and the concept is fundamental in understanding parts of a circle's area in geometry.

Radians

Radians are a unit of angular measure used in mathematics, where one radian is the angle subtended by an arc whose length is equal to the radius of the circle. This measure is preferred in many formulas due to its natural relation with the properties of a circle.

Area Formula for a Sector

The area of a sector of a circle is given by the formula A = (1/2) r²?, where r is the radius of the circle and ? is the central angle measured in radians. This formula is essential for calculating the space contained within any given sector.

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