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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.

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Detailed Solution

According to the figure, we draw the diagram as 

A car has two wipers which do not ever overlap. Each wiper has a blade of length  25 cm sweeping through an angle of 115°. Find the total area that is cleaned

 

It is observed that,  Area cleaned at the sweep of blades of each wiper = Area of a sector  with angle 1150 at the center and 

Radius of a circle =  25 cm.

Thus,  Total area cleaned at each sweep of the blades = 2 × Area cleaned at the sweep of each wiper.

Area cleaned at the sweep of each wiper 

= θ/3600 ×πr2

= 1150/3600 × π × 25 × 25

= 23/72 × 625π

Here, we multiply it by 2 

Total area cleaned at each sweep of the blades = 2× 23/72 × 625π

= 2× 23/72 × 22/7 × 625

= (23 × 11 × 625)/(18 × 7)

= 158125/126

= 1254.96 cm2

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