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A spherical balloon is being inflated at a constant rate of 25 cm³/sec. Explain how the radius and volume of the balloon change over time.

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Final answer:

The volume of the balloon increases at a constant rate, while the radius increases faster as the balloon inflates.

Step-by-step explanation:

In this scenario, the volume of the balloon is changing as it is being inflated. The rate at which the balloon is being inflated is given as 25 cm³/sec. To understand how the radius and volume of the balloon change over time, we need to know the relationship between them.

The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius of the sphere.

Since the balloon is being inflated at a constant rate, the change in volume with respect to time is constant. This means that as time passes, the volume of the balloon increases at a constant rate. However, since the volume of a sphere is proportional to the cube of its radius, the radius of the balloon will not increase at a constant rate. Instead, it will increase faster as the balloon inflates.

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