Question

What is the area of a sectorwhen r= 2/3and 0= /6radians?

Answer 1

ANSWER

$\text{ The area of the sector = }\frac{\text{ }\pi\text{ }}{\text{ 27}}\text{ sq units}$

EXPLANATION

Given that;

$\begin{gathered} \text{ The radius of the circle = }\frac{\text{ 2}}{\text{ 3}} \\ \theta\text{ = }\frac{\pi}{\text{ 6}}\text{ radians} \end{gathered}$

Follow the steps below to find the area of the sector

Apply the area of a sector formula

$\text{ Area of a sector = }\frac{\text{ }\theta\text{ }}{\text{ 360}}\times\text{ }\pi r^2$

Convert radians to degree

$\text{ Recall, 1}\pi\text{ = 180}\degree$$\begin{gathered} \text{ }\theta\text{ = }\frac{\text{ 180}}{\text{ 6}} \\ \text{ }\theta\text{ = 30}\degree \end{gathered}$$\begin{gathered} \text{ Area of a sector = }\frac{\text{ 30}}{\text{ 360}}\text{ }\times\text{ }\pi\text{ \lparen}\frac{2}{3})^2 \\ \\ \text{ Area of a sector = }\frac{\text{ 30}}{\text{ 360}}\text{ }\times\text{ }\frac{4}{9}\pi \\ \\ \text{ Area of a sector = }\frac{\text{ 3 }\times\text{ 4}}{\text{ 36 }\times\text{ 9}}\pi \\ \\ \text{ Area of a sector = }\frac{\text{ 3}}{\text{ 9 }\times\text{ 9}}\pi \\ \\ \text{ Area of a sector = }\frac{\text{ }\pi}{\text{ 27}}\text{ sq units} \end{gathered}$