Question

Find the exact area of the sector of the circle.

Answer 1

We are asked to determine the area of the sector of a circle with a redius of 9 meters and an angle of 90 degrees. To do that we will use the following formula:

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

Where:

`\begin{gathered} r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}`

We have that 90 degrees in radians are equivalent to:

`\theta=(\pi)/(2)`

Substituting the values in the formula:

`A=(1)/(2)(9m)^2((\pi)/(2))`

Solving the operations:

`A=(81\pi)/(4)\approx63.62m^2`

Therefore, the area is approximately 63.62 square meters.