A sphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is H inches above the first plane. The resulting portion of the sphere between the two planes is called a spherical segment; see the picture: In Math 125, you will show that the volume V of the spherical segment is given by this formula (which we will assume): V = (π/3)H(27 – H2). Give EXACT ANSWERS to the questions below. (a) Find the volume of the spherical segment if H=1: (b) Find the rate of change of the volume with respect to H of the spherical segment at H=1: (c) Use the tangent line approximation at H=1 to estimate the value of H that will yield a spherical segment having volume 25 cubic inches:
