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A car has two wipers which do not overlap. Each wiper has a blade of length $21 cm$ sweeping through an angle $120 ° .$ Find the total area cleaned at each sweep of the blades.

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924 cm

920 cm

None of these

930 cm

answer is A.

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Detailed Solution

Given that, a car has two wipers which do not overlap and each wiper has a blade of length 21 cm sweeping through an angle

120 °

.
We know that, the area of sector is

θ 360 ° × π r 2

, where

θ

is the angle subtended at the centre of the circle.
Calculating the area swept by the wipers using the area of sector.

θ 360 ° × π r 2 = 120 ° 360 ° × 227 × 212

\Rightarrow

462 cm

2

Multiply the area swept by 2, since car has 2 wipers.

2 \times 462 = 924 {cm}^{2}

Therefore, total area cleaned at each sweep of the blades is 924

{cm}^{2}

.
Hence the correct option is 1.

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