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

1.	The perimeter of a sector of the circle of area 64π sq.cm is 56 cm. Find the area of the sector.
Answer» Area of circle = πr² But area is given to be 25π sq.cm. ∴ 64π = πr² ∴ r² = 64 ∴ r = 8 cm Perimeter of sector = 2r + S But perimeter is given to be 20 cm. ∴ 56 = 2(5) + S ∴ 56 = 16 + S ∴ S = 40 cm Area of sector = 1/2 x r x S = 1/2 x 8 x 40 = 160sq.cm.

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

Answer»

Area of circle = πr²

But area is given to be 25π sq.cm.

∴ 64π = πr²

∴ r² = 64

∴ r = 8 cm

Perimeter of sector = 2r + S

But perimeter is given to be 20 cm.

∴ 56 = 2(5) + S

∴ 56 = 16 + S

∴ S = 40 cm

Area of sector = 1/2 x r x S

= 1/2 x 8 x 40

= 160sq.cm.