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 = 29.2 m, θ = 5π/6 radians

검증된 단계별 안내

Recall the formula for the area of a sector of a circle: \(\text{Area} = \frac{1}{2} r^{2} \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.

Identify the given values: radius \(r = 29.2\) meters and central angle \(\theta = \frac{5\pi}{6}\) radians.

Substitute the given values into the formula: \(\text{Area} = \frac{1}{2} \times (29.2)^{2} \times \frac{5\pi}{6}\).

Simplify the expression step-by-step: first calculate \(r^{2} = (29.2)^{2}\), then multiply by \(\frac{5\pi}{6}\), and finally multiply by \(\frac{1}{2}\).

After simplifying, round the final result to the nearest tenth to express the area of the sector.

비슷한 문제에 대한 검증된 영상 답변:

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 a portion of the circle's total area, determined by the central angle. It is calculated using the formula A = (1/2) * r² * θ, where r is the radius and θ is the central angle in radians. This formula directly relates the angle to the fraction of the circle's area.

Radian Measure

Radians measure angles based on the radius of a circle, where one radian equals the angle subtended by an arc equal in length to the radius. Using radians simplifies formulas in trigonometry and geometry, such as the sector area formula, which requires the angle to be in radians for direct application.

Rounding and Approximation

After calculating the area, results often need to be rounded to a specified precision, such as the nearest tenth. This involves using decimal approximation of π and performing arithmetic carefully to ensure the final answer meets the required accuracy.