The surface area of a sphere of radius r is S = 4πr2. Its volume is

/in /by

The surface area of a sphere of radius r is S = 4πr2. Its volume is

V = 4πr3/3.

  1. Use MuPAD to find the expression for dS/dV.
  2. A spherical balloon expands as air is pumped into it. What is the rate of increase in the balloon’s surface area with volume when its volume is 30 in.3?

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