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

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 ✎ If

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

= 12 , find the rate of change of the surface area, , when *r*= 5 cm.Describe what happens to the balloon when

is negative.

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

Substitute the given information and solve.

Using just geometry, write the equation for the Surface Area of a generic spherical balloon: *A* = 4π*r*²

What does a negative rate represent?