A sphere of radius 3 inches is sliced with two parallel planes: one passes through the equator and the other is H inches above t
he 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:
1 answer:
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Answer: D.
Step-by-step explanation: Once you subtract from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as
), you end up with
, which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just
.
