(a) well, the radius is 4, so 0<=h<=8
(b) the domain is all real numbers; in this context, clearly see (a)
see google for codomain
(c) these are all just volumes of water at various heights. Naturally, with a radius of 4, f(8) is the volume when full. You can check to see that it is indeed 4/3 πr^3
Consider a spherical tank of radius 4 m that is filling with water. Let V be the volume of water in the tank (in cubic meters) at a given time, and h the depth of the water (in meters) at the same time. It can be shown using calculus that V is a function of h according to the rule
V = f (h) = π/3*h^2(12 − h).
a. What values of h make sense to consider in the context of this function? What
values of V make sense in the same context?
b. What is the domain of the function f in the context of the spherical tank? Why?
What is the corresponding codomain? Why?
c. Determine and interpret (with appropriate units) the values f (2), f (4), and f (8).
What is important about the value of f (8)?
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