9.2k views
5 votes
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.

1 Answer

7 votes

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.

User Dvir Samuel
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.