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Math Help - another problem in radian

  1. #1
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    another problem in radian

    Please help me to solve this.

    In the diagram, http://farm3.static.flickr.com/2255/...474b2ea3_m.jpg
    AD and BC are arcs of circles with centre O, such that OA = OD = r cm, AB = DC = 8 cm and angle BOC = θ radians.

    Given that the area of the shaded region is 48 cm^2, show that r = 6/θ 4.
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  2. #2
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    Hello, geton!

    Are you familiar with the formula for the area of a sector? . A \;=\;\frac{1}{2}r^2\theta


    \text{In the diagram: }AD\text{ and }BC\text{ are arcs of circles with centre }O,
    \text{such that: }\:OA = OD = r,\;AB = DC = 8,\;\text{ and }\;\angle BOC = \theta\text{ radians.}

    \text{Given that the area of the shaded region is }48\text{ cm}^2\text{, show that: }\: r \:= \:\frac{6}{\theta}- 4

    The area of sector AOB \:=\:\frac{1}{2}r^2\theta

    The area of sector BOC \:=\:\frac{1}{2}(r+8)^2\theta

    Their difference is: . A \:=\:\frac{1}{2}(r+8)^2\theta - \frac{1}{2}r^2\theta \:=\:48

    . . . . . Solve for r.

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