(Continuation of Exercise 59) If the sphere has radius R, the volume of water is V = π (Rh² − 1/3 h³), where h is the water level. Assume the level rises at a constant rate of 1 (i.e., h = t).
(a) Find the inflection point of V. Does this agree with your conclusion in Exercise 59?
(b) Plot V for R = 1.

Data From Exercise 59

Water is pumped into a sphere of radius R at a variable rate in such a way that the water level rises at a constant rate (Figure 20). Let V(t) be the volume of water in the tank at time t. Sketch the graph V (approximately, but with the correct concavity). Where does the point of inflection occur?

Transcribed Image Text:

FIGURE 20 h R