Question

A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240c. If another circle of the area same as the sector is formed, then radius of the new circle is [1] (a) 79.5 cm (b) 81.5 cm (c) 83.4 cm (d) 88.5 cm

Answer 1

The radius of the new circle formed would be 81.5 cm

For a circle with radius r, the area of any sector is given by:

Area = πr² * (θ/360)

Given angle of sector is 240 and radius of circle is 100  cm

Area = π *(100)² *(240/360) =π *(100)² *(2/3 )

This would be equal to the area of the new circle:

Let the radius of new circle be R:

Area = πR²

equating the areas:

π *(100)² *(2/3 ) = πR²

R² = 100*100*2/3

R = 100 * √(2/3 ) =  100* 0.816 cm

R = 81.6 cm

Answer 2

Answer:

The Radius of the new circle is :

Area of the sector is : \frac{Central angle made by the sector }{360 deg} X \pi Xr^{2}  

\frac{240 deg }{360 deg} X \pi X100^{2} =  144.7202509

Now this area is equal to the new area of the circle

radius = \sqrt \frac{240X100X100}{360}

= 81.64965 cm