The circle shown with radius 3 has a sector with a central angle of 160. What is the area of the sector?

Identify Formula: Identify the formula to calculate the area of a sector. The area of a sector of a circle is given by the formula A = (θ/360) * π * r^2, where θ is the central angle in degrees and r is the radius of the circle.Plug Values: Plug the given values into the formula. Given that the central angle θ is 160 degrees and the radius r is 3, we can substitute these values into the formula to find the area of the sector. A = (160/360) * π * 3^2Simplify and Calculate: Simplify the fraction and calculate the area. A = (4/9) * π * 9 A = 4 * πCalculate Numerical Value: Calculate the numerical value of the area. Since π is approximately 3.14159, we can calculate the area as follows: A = 4 * 3.14159 A ≈ 12.56636

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Algebra 2

Find the radius or diameter of a circle

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Q. The circle with radius

3

has a sector with a central angle of

160

degrees. What is the area of the sector?

Identify Formula: Identify the formula to calculate the area of a sector. $\newline$ The area of a sector of a circle is given by the formula $A = (\frac{\theta}{360}) \times \pi \times r^2$ , where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.
Plug Values: Plug the given values into the formula. $\newline$ Given that the central angle $\theta$ is $160$ degrees and the radius $r$ is $3$ , we can substitute these values into the formula to find the area of the sector. $\newline$ $A = (\frac{160}{360}) \cdot \pi \cdot 3^2$
Simplify and Calculate: Simplify the fraction and calculate the area. $\newline$ $A = \left(\frac{4}{9}\right) \cdot \pi \cdot 9$ $\newline$ $A = 4 \cdot \pi$
Calculate Numerical Value: Calculate the numerical value of the area. $\newline$ Since $\pi$ is approximately $3.14159$ , we can calculate the area as follows: $\newline$ $A = 4 \times 3.14159$ $\newline$ $A \approx 12.56636$