Question

Which is an expression in terms of Pi that represents the area of the shaded part of K

Answer 1

The shaded part of the circle is the larger sector:

`\begin{gathered} \text{The angle subtended by the larger sector by the center is} \\ 360^0-60^0=300^0\text{ (sum of angles at a point is 360 degr}ees) \end{gathered}`

The area of a sector is given by the formula:

`\begin{gathered} A=(\theta)/(360)*\pi r^2 \\ \theta=300^0 \\ r=x \end{gathered}`

Hence,

`\begin{gathered} A=(300)/(360)*\pi x^2 \\ =(5)/(6)\pi x^2 \end{gathered}`