4. The surface area A of a sphere with radius r is given by the geometric equation A = 4ar². (a) What do the differentials 4 and represent in words? (b) Differentiate both sides of the geometric equation with respect to time to get a relationship between the differentials A and 4. (c) In class, we used the formula V = Tr3 for the volume of a sphere to find the relationship AP = T. 4ar? . Suppose a balloon is being inflated at a rate of a cm³ per second, so Compute the differential 4. AP (d) What is the rate of change of the surface arca of the balloon when the radius is 8cm? (c) As time passes, the balloon is inflated, and the radius r increases. What happens to A over time? Docs this match your intuition? dt

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.