Question

If a sector of a circle has area 100 cm,
then the perimeter of this sector is
(2) 2r
(d) 2 + 200
(6) 2+ 200
(c) 2r + 200​

Answer 1

The perimeter of the sector of the circle will be equal to (2r + 200/r).

• Area of a sector of the circle of angle x and radius r =xr²/2
• Perimeter of the curved surface of the sector of the circle= xr
• Given, xr²/2=100 ⇒xr=200/r
• Perimeter of the sector of the circle = 2r + 200/r
• If r = 1 , then perimeter of the sector of the circle will be equal to 2+200.

Answer 2

Given:

• Area  of a sector of a circle  $100 cm^2$

To Find:

• The perimeter of the sector

Solution:

        Area  of a sector of a circle  $100 cm^2$

      Area of a sector of the circle of angle $\theta$ and radius $r$ is

                    $A = \frac{ \theta r^2}{2}$

                 $100 = \frac{ \theta r^2}{2}$

                $\theta r = \frac{ 200}{r}$

Perimeter of the curved surface of the sector of the circle is given by,

                     $P = \theta r$

                    $P = \frac{ 200}{r}$

Perimeter of the sector of the circle is

                $P = 2r + \frac{ 200}{r}$

Thus, The perimeter of this sector is ​$P = 2r + \frac{ 200}{r}$