Question

what is the area of a sector in a circle of radius 10cm . if the angle between the radii is 60°

Answer 1

AnswEr:-

Your Answer Is 52.3 cm².

ExplanaTion:-

Given:-

• Radius of the sector = 10 cm.

• Angle between the two radii of the sector = 60°.

To Find:-

• The Area of the sector.

Formula Used:-

↦ Area of sector = $\dfrac{\theta}{360°}\times\pi r^2$.

Where,

• Theta is the angles between the two radii of the sector.

• r = Radius of the circle.

So Here,

• $\tt\pi$ = 3.14.

• r = 10 cm.

• $\tt\theta$ = 60°

Now,

Lets find the area by applying the above formula,

↦ Area of sector

$\tt = \dfrac{\theta}{360\degree} \times \pi {r}^{2} . \\ \\ \tt =\cancel \frac{60\degree}{360\degree} \times 3.14 \times 10 \: cm \times 10 \: cm. \\ \\ \tt = \frac{1}{6} \times 3.14 \: \times 100 {cm}^{2} . \\ \\ \tt = \frac{1}{6} \times 314 {cm}^{2} . \\ \\ \tt = \frac{314}{6} \: cm {}^{2} . \\ \\\tt =52. \bar{3} \: cm {}^{2} \\ \\ \tt = 52.3 \: cm {}^{2} (approx).$

$\tt\therefore$ The required area of the sector is 52.3 cm².

Answer 2

Given ,

Radius of circle (r) = 10 cm

Centre angle $(\theta)$ = 60

We know that , the area of sector is given by

$\large \sf \fbox{Area = \frac{ \theta}{360} \times \pi {r}^{2} }$

Thus ,

$\sf \mapsto Area = \frac{60}{360} \times \frac{22}{7} \times {(10)}^{2} \\ \\ \sf \mapsto Area = \frac{2200}{42} \\ \\ \sf \mapsto Area = 52.3 \: \: {cm}^{2}$

$\sf \therefore \underline{The \: area \: of \: sector \: is \: 52.3 \: {cm}^{2} </p><p> }$