A balloon, which always remains spherical on inflation, is...

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15 \mathrm{~cm}$.

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Key Concepts

Volume of a Sphere

This concept involves understanding that the volume of a sphere is given by the formula V = (4/3)?r³, where r is the radius. It is foundational in calculating how the volume of a sphere changes when the radius changes, which is particularly important in problems concerning the inflation or deflation of spherical objects.

Related Rates

Related rates problems connect the rates at which different quantities change with respect to time. By establishing relationships between measurable quantities via an equation (such as the volume to radius relationship in a sphere), one can differentiate with respect to time to determine how one rate of change affects another.

Chain Rule

The chain rule is a fundamental concept in differential calculus that allows the differentiation of composite functions. In the context of related rates, it is used to differentiate functions where one variable is indirectly related to time through another variable, such as differentiating the volume of a sphere with respect to time via its dependence on the radius.

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