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This is urgent, my test is due in an hour, please help me solve this math problem?

Air is being pumped into a spherical balloon at a rate of 10 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 25 cm.

1 Answer

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  • 2 weeks ago

    diameter = 25 means radius = 12.5

    volume at that radius = 4/3 pi*r^3 = 8181.2308

    dV/dt = 10

    V = 4/3 pi r^3

    dV/dt = 4 pi r^2 dr/dt

    plug in 10 for dV/dt and 12.5 for r

    10 = 4 pi (12.5)^2 dr/dt

    dr/dt = 0.00509 cm/s

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