Question

A sector is cut from a circular sheet of radius 100cm, the angle of the sector being 240. If another circle of the area same as the sector is formed, then radius of the new circle is ?
√6 = 2.4, √3 = 1.73

Answer 1

Step-by-step explanation:

Area of the circle= $πr^2$

area of the sector =$πr^2*({\frac{240}{360}})$

=$π*(1)^2*2/3$

Equating it with area of new circle

$2π/3=πR^2$

we get R=$\sqrt{ \frac{2}{3} }$

=.816$m^2$

Answer 2

Answer:

The radius of the new circle = 83.33 cm

Step-by-step explanation:

Given:

radius = r = 100cm

angle of sector = β = 240 degrees

Area of sector = π * r² * (β/360)

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

                        = π * (100)² * (4/6)

Let "R" be the radius of new circle.

We need to find "R" such that area of the new circle = π * (100)² * (4/6)

=> π * R² = π * (100)² * (4/6)

=> R² = (100)² * (4/6)

=> R = 100 * $\sqrt{\frac{4}{6}}$

=> R = 100*(2/$\sqrt{6}$)

=> R = 100*(2/2.4)

=> R = 200/2.4

=> R = 83.33 cm

The radius of the new circle = 83.33 cm