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,

$A=\frac{\theta}{360}\cdot\frac{\pi d^2}{4}$

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

$\begin{gathered} A=\frac{60}{360}\cdot\frac{\pi x^2}{4} \\ =\frac{1}{6}\cdot\frac{\pi x^2}{4} \\ =\frac{\pi x^2}{24} \end{gathered}$

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

Answer: Option B