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Thread: Expansion of Area of Circle

  1. #1
    Junior Member
    Oct 2009

    Expansion of Area of Circle

    A circular cloud of poison gas from a factory explosion is expanding so that t hours after the explosion the radius of the cloud is meters. How fast is the area of the cloud increasing 4 hours after the explosion?
    ________________________square meters per hour

    I've tried about 11 different answers and none of them have worked out, help?
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  2. #2
    Dec 2008
    Auckland, New Zealand
    The area of the cloud (circle) is $\displaystyle A = \pi r^2$

    Substitute R(t) into the formula to get $\displaystyle A(t) = \pi (50+20t)^2$

    Differentiate A(t) with respect to t, then substitute t=4 into your equation for $\displaystyle \frac{dA}{dt}$ to get your answer in square metres per hour.
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