Question

The radius of a sphere, r, is given by the formula below, where s is the surface area of the sphere. A spherical balloon has a maximum surface area of 1,500 square centimeters. Use the given formula to write a function, r(s), that models the situation. Then, use the function to predict how the radius of the balloon changes as the balloon is inflated. As the surface area of the balloon increases, the radius of the balloon increases until the maximum surface area is reached. As the surface area of the balloon increases, the radius of the balloon increases without bound. As the surface area of the balloon increases, the radius of the balloon decreases without bound. As the surface area of the balloon increases, the radius of the balloon decreases until the maximum surface area is reached.

Answer 1

The formula for the radius of a sphere is:
r(s) = sqrt[s/(4pi)]
This is based on the formula that s = 4pi*r^2

As can be seen, as the surface area increases, s/4pi increases, and sqrt(s/4pi) will also increase, meaning that the radius will increase. This continues until the balloon reaches the maximum s = 1500 cm^2.

The correct answer is the first choice:
As the surface area of the balloon increases, the radius of the balloon increases until the maximum surface area is reached.