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Math Help - Related Rates Problem

  1. #1
    Affinity
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    Smile Related Rates Problem

    The volume V of a spherical cancer tumor is given by , where x is the diameter of the tumor. It is estimated that the diameter of the tumor is growing at a rate of 0.4 millimeters per day, at the point in time where the diameter is already 10 millimeters. How fast is the volume of the tumor increasing at this time? (Thanks in advance!)
    Last edited by Affinity; November 12th 2006 at 03:10 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Affinity View Post
    The volume V of a spherical cancer tumor is given by , where x is the diameter of the tumor. It is estimated that the diameter of the tumor is growing at a rate of 0.4 millimeters per day, at the point in time where the diameter is already 10 millimeters. How fast is the volume of the tumor increasing at this time? (Thanks in advance!)
    V = \frac{ \pi x^3}{6}

    Thus dV = \frac{ \pi}{6} \cdot 3x^2 dx

    Use dx \approx 0.4 \, mm/day. Then dV \approx 62.832 \, mm^3/day

    -Dan
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