Question

Figure shows a sector of a circle of radius r cm containing an angle θ°. The area of the sector is A cm² and perimeter of the sector is 50 cm.

(i) θ = \(\frac{360}{π}\)\((\frac {25}r - 1)\)

(ii) A = 25r - r²

Answer 1

Given, 

Radius of the sector = r cm 

Angle subtend = θ 

Area of sector = A cm² 

Perimeter of sector = 50 cm 

Area of sector = \(\frac{θ}{360}πr^2\)

Perimeter of sector = \(\frac{θ}{360}2πr + 2r\)

put value of \(\frac{θ}{360}\) from equation first to equation second

area = \(\frac{25 - r}{πr}\)(πr²) = (25 - r)r

Area = 25r - r²