Question

Find the area of a sector of a circle with radius 6 cm if the angle of the sector is $60^\circ $.

Answer 1

Hint: We need to multiply the square of the radius with $\pi = \dfrac{{22}}{7}$ to get the area of the circle. This area of the circle is multiplied with the quotient obtained on dividing $60^\circ $ by $360^\circ $ to get the area of the sector of a circle.


Complete step-by-step solution
We are given a circle with radius 6 cm.
Also, we are given that the angle of a sector of this circle is $60^\circ $.
We are asked to compute the area of this sector of the circle.
Let’s have a look at the figure of this circle.

The shaded portion is the sector for which we are to find the area.
If the angle $\theta $measured in degrees, then the area of the sector of the circle is given by the formula
Area of sector\[ = \dfrac{\theta }{{360^\circ }} \times \pi {r^2}\]
Where r is the length of the radius of the circle and $\theta $ is the angle of the sector.
We have$\theta = 60^\circ $ and $r = 6cm$. Take$\pi = \dfrac{{22}}{7}$.
Therefore, on substituting, we get
Area of sector\[ = \dfrac{{60^\circ }}{{360^\circ }} \times \dfrac{{22}}{7} \times {6^2} = \dfrac{{22}}{7} \times 6 \approx 18.86c{m^2}\]

Hence the required area is \[18.86c{m^2}\].

Note:Students tend to use the formula for area of sector wrongly. Instead of $\pi {r^2}$, they tend to use$2\pi r$in the formula. This will give you the length of the arc and not the area of the sector because $2\pi r$ is the length of the circumference of the circle.