Name: Derek

Who is asking: Student
Level: All

Question:
How can you show that if the volume of a balloon is decreasing at a rate proportional to its surface area, the radius of the balloon is shrinking at a constant rate.

Hi Derek,

If r is the radius of the sphere, V is its volume and S is its surface area, then V = 4/3pi r³ and S = 4 pi r². V, S and r are functions of time t. Since the volume of the balloon is decreasing at a rate proportional to its surface area, dV/dt = k S = k 4 pi r² where k is a constant. Differentiate V implicitly with respect to t and simplify.

Cheers,
Harley