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Question
The perimeter of the sector of the circle of area 64π sq.cm is 56 cm. Find the area of the sector.
Solution
Area of circle = πr2
But area is given to be 64π sq.cm.
∴ 64π = πr2
∴ r2 = 64
∴ r = 8 cm
Perimeter of sector = 2r + S
But perimeter is given to be 56 cm.
∴ 56 = 2(8) + S
∴ 56 = 16 + S
∴ S = 40 cm
Area of sector = `1/2 xx "r" xx "S"`
= `1/2 xx 8 xx 40`
= 160 sq. cm.
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