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Math Help - Rates of Change - Sphere

  1. #1
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    Rates of Change - Sphere

    A metal sphere is dissolving in acid. It remains spherical and the rate at which its volume decreases is proportional to its surface area. Show that its radius is decreasing at a constant rate.
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  2. #2
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    Here's a kick off

    \displaystyle \frac{dV}{dt}\propto 4\pi r^2

    \displaystyle \frac{dV}{dt}= 4k\pi r^2

    \displaystyle \frac{\frac{dV}{dr}}{\frac{dt}{dr}}= 4k\pi r^2

    Now firstly find \displaystyle \frac{dV}{dr} from \displaystyle V = \frac{4}{3}\pi r^3
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  3. #3
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    Thanks, the question looked more difficult than it actually is!
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