Cracking The Ap Calculus ab Exam 2018

water   is  2   inches  deep.

First, rewrite the equation as

V   =   πRh^2   −    h^3

Now, take the derivative of the equation with respect to t.

    =   2πRh    −   πh^2

If we plug in = 4, R = 6, and h = 2, we get

4   =   20π     or      =       =   

(b) Find an expression for r, the radius of the surface of the spherical segment of water, in
terms of h.

Notice that we can construct a right triangle using the radius of the sphere and the radius of the
surface of the water.

Notice that the distance from the center of the sphere to the surface of the water is R − h. Now,
we can use the Pythagorean Theorem to find r.

R^2     =   (R  −   h)^2    +   r^2

We can rearrange this to get

Because R = 6, we get