Question

Question 15 (5 points) This exercise involves the formula for the area of a circular sector. The area of a sector of a circle with a central angle of 100° is 67 m2. Find the radius of the circle. (Round your answer to one decimal place.)

Answer 1

`\begin{gathered} A=(r^2)/(2)\theta \\ \text{Where:} \\ A=\text{Area of the circular sector}=67m^2 \\ \theta=angleinradians=100^(\circ)*(\pi)/(180)=(5)/(9)\pi \\ \end{gathered}`

Solving for r:

`\begin{gathered} 67=(r^2)/(2)(5)/(9)\pi \\ r^2=(67*18)/(5\pi) \\ r=\pm\sqrt[]{76.77634455} \\ r=\pm8.762211168 \\ r\approx8.8 \end{gathered}`