Question

The area of a circle is 81π sq.cm. Find the length of the arc subtending an angle of 300° at the centre and also the area of corresponding sector.

Answer 1

Let 'r' be the radius of a circle whose area is 225 π sq. cm. 

Area of circle = πr²

But area is given to be 81π sq. cm.

∴ πr² = 81π

∴ r² = 81

∴ r = 9 cm

θ = 300°

= `(300 xx pi/180)^c`

= `((5pi)/3)^c`

Since S = r × θ,

S = `9 xx (5pi)/3`

∴ S = 15 π cm

Area of sector = `1/2r^2theta`

= `1/2 xx 9 xx 9 xx (5pi)/3` 

= `1/2 xx 9 xx cancel(9)^3 xx (5pi)/cancel(3)_1`

= `(135 pi)/2` sq. cm