Question

The windscreen wiper of a car sweeps
through an angle of 150°. The blade of the
wiper is 21 cm long and the radius of the
unswept sector is 6 cm.
What area of the windscreen is swept clean?​

Answer 1

Answer:

A ≈ 530 cm²

Step-by-step explanation:

The swept area equals the total area covered by the blade minus the unswept area.

The area of a sector with radius r and angle θ is:

A = (θ / 360) πr²

So the swept area is:

A = (θ / 360) πR² − (θ / 360) πr²

A = (θ / 360) π (R² − r²)

A = (150 / 360) π (21² − 6²)

A ≈ 530 cm²

Answer 2

The area of the windscreen is swept clean is $530 cm^2$

Calculation of the area:

Since The swept area is equivalent to the total area covered by the blade minus the unswept area.

So,

The area of a sector with radius r and angle θ is:

Now

$A = (\theta \div 360) \pi r^2$

So the swept area is:

$A = (\theta \div 360) \pi R^2 - (\theta \div 360) \pi R^2 \\\\A = (\theta \div 360) \pi (R^2 - r^2)\\\\A = (150 \div 360) \pi (21^2 - 6^2)\\\\A = 530 cm^2$

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