Question

The area A of a sector of a circle is given by A=πr²s/360, where r is the radius of the circle and s is the angle measure(in degrees) of the sector. Solve the equation for s to find the angle measure given the radius and area of the circle.

Answer 1

`A= ( \pi r^2s)/(360) \\ \\ \pi r^2s=360A \\ \\ s= (360A)/( \pi r^2)`

Answer 2

Explanation:

It is given that The area A of a sector of a circle is given by:

`A=\frac{{\pi}r^2s}{360}`

where where r is the radius of the circle and s is the angle measure(in degrees) of the sector.

Then, the equation for s can be obtained by rewriting the above given equation, thus

`A=\frac{{\pi}r^2s}{360}`

`{\pi}r^2s=360A`

`s=\frac{360}{{\pi}r^2}`

which is the required equation for s to find the angle measure given the radius and area of the circle.