Question

What is the area of a sectorwhen r:5/6and 0=2/3 radians?

Answer 1

Given:

Radius = 5/6

Angle

`\theta=(2\pi)/(3)\text{ radians}`

Required:

Find the area of the sector.

Step-by-step explanation:

The area of the sector is given by the formula:

`A=(1)/(2)r^2\theta`

Substitute the given values in the formula.

`\begin{gathered} A=(1)/(2)*((5)/(6))^2*(2\pi)/(3) \\ =(1)/(2)*(25)/(36)*(2\pi)/(3) \\ =(25\pi)/(108)\text{ sq unit} \end{gathered}`

Final Answer:

Thus the area of the sector is

`(25\pi)/(108)`