Question

If x represents the diameter of a circle, what is the area of a 60-degree sector of the circle?A. πx^2B. πx^2/24C. πx^2/6D. πx^2/36

Answer 1

The diameter of circle is d = x.

The angle of sector is,

`\theta=60`

The formula for area of sector is,

`A=(\theta)/(360)\cdot(\pi d^2)/(4)`

Substitute the values in the formula to determine the area of sector.

`\begin{gathered} A=(60)/(360)\cdot(\pi x^2)/(4) \\ =(1)/(6)\cdot(\pi x^2)/(4) \\ =(\pi x^2)/(24) \end{gathered}`

So area of sector of circle is πx^2/24.

Answer: Option B