Question

A car has two wipers that do not overlap. Each wiper has a blade with a length of 24cm sweeping through an angle of 111°. Find the total area cleaned with each sweep of the blades​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• A car has two wipers that do not overlap.

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• Each wiper has a blade with a length of 24cm 

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• Angle of sweeping is 111°

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Total area cleaned by 2 wipers

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{We know that ,}}}$

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Area of sector = $\sf \dfrac { \theta } { 360° } \times \pi r ^2$ ---- (1)

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Where Ѳ the angle in degree subtended by the arc at the centre of the circle and r is the radius

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$\underline{\bold{\texttt{Area sweeped by 1 wiper at a time :}}}$

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➠ Ѳ = 111°

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➠ r = 24 cm

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⟮ Putting these values in (1) ⟯

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➜ $\sf \dfrac { 111° } { 360° } \times \pi 24^2$

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$\underline{\bold{\texttt{Area sweeped by 2 wiper at a time :}}}$

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➜ $\sf 2 \times \dfrac { 111° } { 360° } \times \pi 24^2$

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➜ $\sf 2 \times \dfrac { 111° } { 360° } \times \dfrac { 22 } { 7 } \times 24 \times 24$

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➜ $\sf \dfrac { 37 } { 30 } \times 24 \times 24 \times \dfrac { 11 } { 7 }$

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➜ $\sf \dfrac { 37 } { 5 } \times 12 \times 8 \times \dfrac { 11 } { 7 }$

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➜ $\sf \dfrac { 39072 } { 35 }$

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➨ 1116.34 sq. cm

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Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• A car has two wipers that do not overlap.

$\:\:$

• Each wiper has a blade with a length of 24cm 

$\:\:$

• Angle of sweeping is 111°

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Total area cleaned by 2 wipers

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

$\underline{\bold{\texttt{We know that ,}}}$

$\:\:$

Area of sector = $\sf \dfrac { \theta } { 360° } \times \pi r ^2$ ---- (1)

$\:\:$

• Where Ѳ the angle in degree subtended by the arc at the centre of the circle and r is the radius

$\:\:$

$\underline{\bold{\texttt{Area sweeped by 1 wiper at a time :}}}$

$\:\:$

➠ Ѳ = 111°

$\:\:$

➠ r = 24 cm

$\:\:$

⟮ Putting these values in (1) ⟯

$\:\:$

➜ $\sf \dfrac { 111° } { 360° } \times \pi 24^2$

$\:\:$

$\underline{\bold{\texttt{Area sweeped by 2 wiper at a time :}}}$

$\:\:$

➜ $\sf 2 \times \dfrac { 111° } { 360° } \times \pi 24^2$

$\:\:$

➜ $\sf 2 \times \dfrac { 111° } { 360° } \times \dfrac { 22 } { 7 } \times 24 \times 24$

$\:\:$

➜ $\sf \dfrac { 37 } { 30 } \times 24 \times 24 \times \dfrac { 11 } { 7 }$

$\:\:$

➜ $\sf \dfrac { 37 } { 5 } \times 12 \times 8 \times \dfrac { 11 } { 7 }$

$\:\:$

➜ $\sf \dfrac { 39072 } { 35 }$

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➨ 1116.34 sq. cm

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