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    Application of Derivatives and Differentiation : Rate of Change of Volume of a Sphere ( Balloon )

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    Air is being pumped into a spherical balloon so that the radius is increasing at the rate of dr/dt = 3 inches per second. What is the rate of change of the volume of the balloon in cubic inches per second, when r = 8 inches? Hint: V = 4/3(pi)r^3

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    Solution Preview

    We have,

    Volume of the spherical balloon as, V = (4/3) pi r^3

    Now, differentiating it w.r.t time t, we get,

    dV/dt = (4/3) pi *( 3 r^2) * dr/dt ( ...

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