### Home > CALC > Chapter 7 > Lesson 7.1.5 > Problem7-52

7-52.
1. As Khalid inflates a spherical balloon, Kareem wonders about its different rates. He knows that the rate at which Khalid blows is equal to the rate at which the volume changes . As the balloon inflates, other aspects are changing as well, such as the radius and the surface area. Homework Help ✎

1. If = 10, find the rate of change of the radius, , when r = 3 cm.

2. If = 12, find the rate of change of the surface area, , when r = 5 cm.

3. Describe what happens to the balloon when is negative.

Using just geometry (no Calculus), find the equation for a generic spherical balloon.

$V=\frac{4}{3}\pi r^{3}$

Substitute the given information and solve.

$\text{Find }\frac{dr}{dt}, \text{ you will need that information later.}$

Using just geometry, write the equation for the Surface Area of a generic spherical balloon: A = 4πr²

What does a negative rate represent?