Question

The area of a sector of a circle of 6 cm radius is 15π sq.cm. Find the measure of the arc and length of the arc corresponding to the sector.

Answer 1

Final Answer :   Angle of sector: $150\degree$
                            Length of arc of sector: 5πcm 

Steps: 
1) Area of sector : $15\pi cm^{2}$ 
Radius ,r = 6 cm 
We know that , 

Area of sector : 

$\frac{\pi r^{2}\theta}{360\degree} = 15\pi \\ \\ =\ \textgreater \ \frac{6^{2} *\theta}{360} = 15 \\ \\ =\ \textgreater \ \theta = 150\degree$

2)  Length of arc,
$l= \frac{\pi*r*\theta}{180\degree} \\ \\ l = \frac{\pi*6* 150\degree }{180\degree} \\ \\ =\ \textgreater \ l = 5\pi cm$

Answer 2

Hi ,

It is given that ,

Area of the sector ( A ) = 15π sq cm

Radius of the circle ( r ) = 6 cm

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We know that ,

1 ) Area of the sector ( A ) = ( x°/360 ) × πr²

Where , x is sector angle ,

2 ) length of the arc ( l ) = ( x°/360 ) × 2πr

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Now ,

1 ) ( x°/360 ) × πr² = A

( x°/360 ) × π × 6² = 15π

x° = ( 15π × 360 )/( π × 36 )

x° = 150

2 ) length of the arc ( l ) = ( x/360 ) × 2πr

l = ( 150/360 ) × 2 × π × 6

l = 5π cm