MA 141 Study Guide - Final Guide: Pythagorean Theorem
Document Summary
Previously, we had an explicit function r(t) for the radius. However, both volume and radius are changing over time, so we can think of them as v (t) and r(t). Ex: if helium is entering a spherical balloon at the rate of 20 cm3/sec, what is the rate of change of the radius with respect to time, dr dt. We know that volume of a sphere is given by v = We want to nd implicit di erentiation on both sides: dr dt. , the rate of change of the radius with respect to time. We will use d dt (v ) = dv dt. We want rate of change of the radius over time, so solve for dr dt dr dt. Since we are pumping helium in at a rate of 20 cm3/sec, we have need to nd r at the point in question - the value r0 when the volume is 100 cm3.
