The windscreen wiper of a car sweepsthrough an angle of 150°. The blade of thewiper is 21 cm long and the radius of theunswept sector is 6 cm. What area of the windscreen is swept clean?

Answer: 529.675 cm² is swept clean.

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 * πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

Considering the bigger sector,

Radius = length of blade = 21 cm

θ = 150 degrees

Therefore,

Area = 150/360 * 3.14 * 21² = 576.975 cm²

Considering the smaller sector,

Radius = 6 cm

θ = 150 degrees

Therefore,

Area = 150/360 * 3.14 * 6² = 47.1 cm²

The area of the windscreen that is swept clean is

Area of bigger sector - area of smaller sector. It becomes

576.975 - 47.1 = 529.675 cm²