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A car has two wipers that do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the blades. ("Take" π =22/7) - Mathematics

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Sum

A car has two wipers that do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the blades. `("Take" π =22/7)`

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Solution

Radius = r = 21 cm

sweeping angle = 120°

Total area cleaned by two wipers `=2xx "area cleaned by one wiper"`

Total area cleaned by two wipers`=2xx  "area of sector with"  120^@`

`=2 xx theta /360 xx pi"r"^2`

On substituting the values `=2 xx 120/360 xx 22/7 xx(21)^2`

`=2 xx 120/360 xx 22/7 xx 441` 

`= (2 xx 22 xx 147)/7`

`=6468/7 = 924`

Therefore, area cleaned by both wipers is 924 cm2

Concept: Areas of Sector and Segment of a Circle
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