Verified answer

Given :

• Radius = 6 cm

• Angle of sector = 60°

To Find :

• The area of a sector of a circle = ?

Formula used :

[tex]Area \: of \: sector=\frac{θ}{360°} \times\pi{r}^{2} \\ [/tex]

Solution Explanation :

[tex]Area \:=\frac{θ}{360°} \times\pi{r}^{2} \\ \\ = \frac{60}{360} \times \pi \times 6 \times 6 \\ \\ = \frac{{\cancel{60}}}{{\cancel{360}}} \times \pi \times 36 \\ \\ = \frac{1}{6} \times \frac{22}{7} \times 36 \\ \\ = \frac{1}{{\cancel{6}}} \times \frac{22}{7} \times {\cancel{36}} \\ \\ = \frac{22 \times 6}{7} \\ \\ = \frac{132}{7} \: {cm}^{2} [/tex]

We use the formula for the area of the sector of a circle.

The formula for the area of the sector of a circle with radius 'r' and angle θ = (θ/360°) × πr2

Given, θ = 60°, Radius = 6 cm

Area of the sector = (θ/360°) × πr2

= 60°/360° × 22/7 × 6 × 6

= 132/7 cm2