Word Problem-Calculus

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A spherical balloon is being inflated in such a way that its radius increases at a rate of 3 cm/min. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes?

my answer is 45 cm/min.

is this right. thanks

  • Word Problem-Calculus-Already Solved-Please check? -

    Thank you!

  • Word Problem-Calculus -

    way off.
    First, volume is cm^3

    v = 4/3 pi r^3
    dv/dt = 4 pi r^2 dr/dt
    at t=5, r=15 so
    dv/dt = 4 pi * 225 * 3 = 2700 pi cm^3/min

    How did you come up with 45? Way small, and I'd surely expect a pi to appear somewhere in any problem involving a sphere.

  • Word Problem-Calculus -

    My fault lied in plugging in directly. Thank you for showing me the steps.

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