Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.
r = 12.7 cm, θ = 81°

검증된 단계별 안내

Recall the formula for the area of a sector of a circle: \(\text{Area} = \frac{\theta}{360} \times \pi r^{2}\), where \(\theta\) is the central angle in degrees and \(r\) is the radius.

Identify the given values: radius \(r = 12.7\) cm and central angle \(\theta = 81^\circ\).

Substitute the given values into the formula: \(\text{Area} = \frac{81}{360} \times \pi \times (12.7)^{2}\).

Calculate the square of the radius: \((12.7)^{2}\), then multiply by \(\pi\) and the fraction \(\frac{81}{360}\).

After performing the multiplication, round the result to the nearest tenth to express the final area.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Area of a Sector

The area of a sector of a circle is the portion of the circle's area enclosed by two radii and the arc between them. It is calculated using the formula (θ/360) × π × r² when θ is in degrees, where r is the radius and θ is the central angle.

Central Angle in Degrees

The central angle θ is the angle formed at the center of the circle by two radii. It determines the size of the sector and must be expressed in degrees or radians to use the appropriate area formula.

Rounding and Precision

After calculating the area, the result should be rounded to the nearest tenth as specified. This involves understanding decimal places and applying proper rounding rules to present the final answer accurately.

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5.r = 12.7 cm, θ = 81°