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Can you give me step by step instruction on how to solve this problem

Helium is pumped into a spherical balloon at a constant rate of 4cubic feet per second. How fast is the radius increasing after 3 minutes? At what time (if any) is the radius increasing at a rate of 120 feet per second?

  • math -

    given: dV/dt = 4 ft^3/sec

    V= (4/3)πr^3
    dV/dt = 4πr^2 dr/dt

    3 min = 180 sec
    So after 3 min, V = 180(4) or 720 ft^3

    720 = (4/3)πr^3
    solve for r, then sub into
    dV/dt = 4πr^2 dr/dt
    solve for dr/dt

    For the second part, replace dr/dt by 120
    That way you will be able to solve for r
    Using that r, find the Volume,
    divide that volume by 4 to get the number of seconds it took to fill it that much.

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