Question

A car has two wipers which do not ever sap each wiper has a blade of length 34 cm swapping through an angle 105 degree find the total area of cleaner each swap of blades

Answer 1

Solution :-

The Area swept by the Blades will form 2 sectors.

→ Radius of sector = 34cm.

→ Angle At centre = 105° .

So,

→ Required Area of sector = (Angle at centre/360°) * π * (Radius)²

→ Req. Area = (105°/360°) * (22/7) * 34 * 34

→ Req. Area = (21/72) * (22/7) * 34 * 34

→ Req. Area = (3/72) * 22 * 34 * 34

→ Req. Area = (1/24) * 22 * 34 * 34

→ Req. Area = (1/12) * 11 * 34 * 34

→ Req. Area = (1/6) * 11 * 17 * 34

→ Req. Area = (1/3) * 11 * 17 * 17

→ Req. Area = (3179/3)

→ Req. Area ≈ 1059.67 cm². (Ans.)

Hence, The Total Area swept by the Blades is 1059.67cm².

Answer 2

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QUESTION :-

A car has two wipers which do not ever sap. Each wiper has a blade of length 34 cm swapping through an angle 105°. Find the total area of cleaner on each swap of blades.

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SOLUTION :-

GiveN :-

• Length of each blade = 34 cm

• Angle respective to which each wiper swaps = 105°

TO FinD :-

$\longmapsto$ The total area of cleaner on each swap of blades.

AcknowledgemenT :-

• The two blades form two sectors of a circle with radius(r) 34 cm, when they move while swapping.

• Area of a sector = (Angle at centre/360°) * πr²

CalculatioN :-

Putting the known values in the formula above :-

$\displaystyle{\sf{Area=\frac{105^\circ}{360^\circ} \times \pi (34)^2}}\\\\\displaystyle{\sf{\implies Area=\frac{105^\circ}{360^\circ}\times \frac{22}{7}\times 1156 }}\\\\\displaystyle{\sf{\implies Area=\frac{15}{360}\times 22\times 1156 }}\\\\\displaystyle{\sf{\implies Area=\frac{1}{24}\times 22\times 1156 }}\\\\\displaystyle{\sf{\implies Area=\frac{11}{12}\times 1156 }}\\\\\displaystyle{\sf{\implies Area=\frac{12716}{12} }}\\\\\boxed{\displaystyle{\sf{\implies Area=1059.66\ cm^2 }}}$

$\leadsto$ So, the area covered by EACH blade is 1059.66 cm².

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Regards from

CunningKing :)