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Math Help - rate change word problem

  1. #1
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    rate change word problem

    So I'm having trouble starting this problem.

    A spherical snowball is melting in such a way that its radius is decreasing at the rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 8 cm?

    Any suggestions?
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  2. #2
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    Volume of the sphere V = 4/3*π*r^3
    dV/dt = 4/3*π*3*r^2*dr/dt.
    Substitute the values to get the result.
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  3. #3
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Volume of the sphere V = 4/3*π*r^3
    dV/dt = 4/3*π*3*r^2*dr/dt.
    Substitute the values to get the result.
    You're right for sure, but this is under Geometry, and dv/dt is a Calculus concept!
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  4. #4
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    Quote Originally Posted by PeltierC View Post
    You're right for sure, but this is under Geometry, and dv/dt is a Calculus concept!
    Then you can do this way.
    Vf - Vi = ΔV = 4/3*π*[ (R+ΔR)^3 -R^3]
    Using the factorization of (a^3 - b^3) simplify the above equation. Then find ΔV/Δt.
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