Question

Radius of a circle is 10cm. measure of an arc of the circle is 54°.find the area of the sector associated with the arc.​

Answer 1

Radius of the circle ( r ) = 10 cm

Arc of the circle = 54°

Area of the sector = ( x/360 ) × πr²

A = ( 54/360 ) * 3.14 * 10²

A = 47.1 cm²

Therefore ,

Area of the sector = A = 47.1 cm²

Answer 2

Given ,

Radius of circle (r) = 10 cm

Degree measure $\sf( \theta)$ = 54°

We know that ,

$\large \fbox{ \fbox{ \sf \: Area \: of \: sector = \frac{ \theta}{360} \times \pi {(r)}^{2} \: }}$

$\sf Area = \frac{\cancel {56}}{360} \times \frac{22}{\cancel 7} \times {(10)}^{2} \\ = \frac{8}{ \cancel{360}} \times \cancel {2200 }\\ \\ \sf = \frac{8}{180} \times 1100 \\ \\\sf = \frac{8800}{180} \\ \\\sf = 48.88 \: \: {cm}^{2} \: \: \{ approx\}$

Hence , 48.88 cm² is the area of given sector