Question

A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240degree. If another circle of the area same as the sector is formed, then radius of the new circle is

Answer 1

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

Answer 2

The radius of new circle is 81.6 cm.

Step-by-step explanation:

Consider the provided information.

A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240degree.

Area of sector of a circle is: $\frac{\theta}{360^0}\pi r^2$

Substitute the respective value.

$A=\frac{240^0}{360^0}\pi (100)^2$

$A=\frac{2}{3}\pi (100)^2$

$A=\frac{20000\pi}{3}$

If another circle of the area same as the sector is formed, then radius of the new circle is

Area of circle is: $\pi r^2$

$\frac{20000\pi}{3}=\pi r^2$

$\frac{20000}{3}=r^2$

$r=\sqrt{\frac{20000}{3}}$

$r\approx 81.6$

Hence, the radius of new circle is 81.6 cm.

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