Question

measure of angle RST = 142 degrees. The area of the shaded sector is 11.15 cm squared. What is the radius of the circle? round to nearest tenth.

Answer 1

Given data:

The given angle is ∠RST=142 degrees.

The area of the shaded region is A=11.15 cm squared.

The expression for the area of the shaded region is,

`A=(\angle RST)/(360^(\circ))\pi(r)^2`

Substitute the given values in the above expression.

`\begin{gathered} 11.5cm^2=(142^(\circ))/(360^(\circ))\pi(r)^2 \\ r=3.046\text{ cm} \\ \approx3.0\text{ cm} \end{gathered}`

Thus, the radius of the circle is 3 cm.