AREAS RELATED

TO CIRCLE

• Sums based on Area of sector

80°

17. To warn ships for underwater rocks, a lighthouse spreads

a red coloured light over a sector of angle 80°

to a distance of 16.5 km.

Find the area of the sea over which the ships are warned. (Use π = 3.14)

16.5km

A

B

X

O

What is the formula to find area of sector?

Sol.

?

Radius (r) = 16.5 km

✔

?

✔

Central angle (θ) = 80º

=

×

3.14

×

2

9

=

×

×

=

3

55

1

55

=

189.97 km²

80°

17. To warn ships for underwater rocks, a lighthouse spreads

a red coloured light over a sector of angle 80°

to a distance of 16.5 km.

Find the area of the sea over which the ships are warned. (Use π = 3.14)

Area of sector is 189.97 km²

∴

=

1899700

10000

25 cm

Q. A car has two wipers which do not overlap. Each wiper has a

blade of length 25 cm sweeping through an angle of 115°.

Find the total area cleaned at each sweep of the blades.

115º

115º

Q. A car has two wipers which do not overlap. Each wiper has a

blade of length 25 cm sweeping through an angle of 115°.

Find the total area cleaned at each sweep of the blades.

Sol.

r = 25 cm

=

115

360

×

22

7

× 25

× 25

Total area

2 ×

=

158125

126

cm²

θ = 115º

∴

ar(O-AXB)

=

=

23

36

×

11

7

× 25

× 25

=

23

36

×

11

7

× 25

× 25

∴

=

23

18 × 7

× 11

× 25

Total area

∴

area of sector =

1254.96

=

O

A

X

B

23

72

11

36

× 25

18