Question

The perimeter of the sector of the circle of area 64π sq.cm is 56 cm. Find the area of the sector.

Answer 1

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.