Question

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

Answer 1

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

Step-by-step 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}}*\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{ }*\text{ }\pi\text{ \lparen}(2)/(3))^2 \\ \\ \text{ Area of a sector = }\frac{\text{ 30}}{\text{ 360}}\text{ }*\text{ }(4)/(9)\pi \\ \\ \text{ Area of a sector = }\frac{\text{ 3 }*\text{ 4}}{\text{ 36 }*\text{ 9}}\pi \\ \\ \text{ Area of a sector = }\frac{\text{ 3}}{\text{ 9 }*\text{ 9}}\pi \\ \\ \text{ Area of a sector = }\frac{\text{ }\pi}{\text{ 27}}\text{ sq units} \end{gathered}`