Question

The perimeter of a sector of circle of area 25πsq.cm is 20 CM find the area of sector

Answer 1

get the radius and length of arc

Answer 2

Area of sector = 50 Cm²

Step-by-step explanation:

Given:

Perimeter of a sector = 20 cm

Area of a circle = 25$\pi$ cm²

Computation:

Area of a circle = 25$\pi$ cm²

$\pi r^2 =$ 25$\pi$ cm²

$r^2 = 25\\\\ r = \sqrt{25} \\\\r = 5$

Perimeter of a sector = 20 cm

$\frac{\theta}{360}2\pi r = 20\\\\\frac{\theta}{360}\times2\times\frac{22}{7}\times 5= 20\\\\\frac{\theta}{360}\times\frac{220}{7} = 20\\\\ \frac{\theta}{360} = \frac{140}{220}\\\\ \theta = \frac{2520}{11}$

Area of sector

$\frac{\theta}{360}\pi r^2\\\\ \frac{2520}{11}\times \frac{1}{360}\times \frac{22}{7}\times5\times5\\\\ 50 cm^2$

Area of sector = 50 Cm²

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