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Melting Snowball: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. (Hint: Surface Area =4(pi)r^2)

  • calculus -

    dV/dt = kA.

    V = (4/3) π r^3 and A = 4 π r^2

    dV/dt = d/dt((4/3) π r^3) = (4/3) π 3 r^2 (dr/dt)

    Now let's plug that into the first equation:

    (4/3) π 3 r^2 (dr/dt) = k A = k(4 π r^2) = 4 π k r^2

    So when we simplify by dividing left and right sides by 4 π r^2, we get:

    dr/dt = k

    which is saying exactly what we wanted to prove: that dr/dt is constant.

  • calculus -

    Steve you are so smart. thank you. you don't how much it helped me. you save my life from this MMAD MATH INSTRUCTOR

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