if the perimeter of a sector of a circle, of area 25 pi sq. cm is 20 cm. Find the area of sector

Answers (1)
M manish

We have,
Area of circle = \pi.\ r^2 = 25\ \pi.
Therefore, r = \sqrt{25} = 5

 

P of sector = 20 cm
                  = 2r + r\times \theta
          \\20 =10 + 5\times \theta\\ 10 = 5 \theta

Therefore, \theta = 2

 

Now the area of a sector is given as
=\left ( \frac{\theta}{360^0} \right )\times \pi\times r^2
=\left ( \frac{2}{360^0} \right )\times \pi\times 5^2
=\left ( \frac{1}{180^0} \right )\times \pi\times 25

 

Thus, the area of the sector is 25 sq.cm


 

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