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

Key Concepts

Area of a Sector

The area of a sector of a circle is a portion of the circle defined by a central angle. It can be calculated using the formula A = 0.5 * r^2 * θ, where A is the area, r is the radius, and θ is the angle in radians. This formula derives from the relationship between the angle and the total area of the circle.

Radians

Radians are a unit of angular measure used in mathematics. One radian is the angle formed when the arc length is equal to the radius of the circle. In this context, the angle θ is given in radians, which is essential for using the area formula correctly, as it directly relates to the circle's geometry.

Rounding to the Nearest Tenth

Rounding to the nearest tenth involves adjusting a number to one decimal place. This is important in providing a clear and concise answer, especially in practical applications like measuring area. The process includes looking at the hundredths place to determine whether to round up or down.