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    The straight metal arm of a windscreen wiper on a car rotates in a circular motion from a pivot point, O, through an angle of 140°. The windscreen is cleared by a rubber blade of length 46 cm that is attached to the metal arm between points A and The total length of the metal arm, OB, is 56 cm. The part of the windscreen cleared by the rubber blade is shown unshaded in the following diagram.

    Question
    SLPaper 1

    The straight metal arm of a windscreen wiper on a car rotates in a circular motion from a pivot point, O, through an angle of 140°. The windscreen is cleared by a rubber blade of length 46 cm that is attached to the metal arm between points A and The total length of the metal arm, OB, is 56 cm. The part of the windscreen cleared by the rubber blade is shown unshaded in the following diagram.

    1.

    Calculate the length of the arc made by B, the end of the rubber blade.

    [2]
    Verified
    Solution

    attempt to substitute into length of arc formula 140∘360∘×2π×56\frac{140^\circ}{360^\circ} \times 2\pi \times 56360∘140∘​×2π×56 (M1) 137 cm(136.833…,392π9 cm)137 \text{ cm} (136.833\ldots, \frac{392\pi}{9} \text{ cm})137 cm(136.833…,9392π​ cm) (A1)

    2.

    Determine the area of the windscreen that is cleared by the rubber blade.

    [3]
    Verified
    Solution

    subtracting two substituted area of sectors formulae (M1) (140∘360∘×π×562)−(140∘360∘×π×102)(\frac{140^\circ}{360^\circ} \times \pi \times 56^2)-(\frac{140^\circ}{360^\circ} \times \pi \times 10^2)(360∘140∘​×π×562)−(360∘140∘​×π×102) OR 140∘360∘×π×(562−102)\frac{140^\circ}{360^\circ} \times \pi \times (56^2-10^2)360∘140∘​×π×(562−102) (A1) 3710 cm2(3709.17… cm2)3710 \text{ cm}^2 (3709.17\ldots \text{ cm}^2)3710 cm2(3709.17… cm2) (A1)

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