Question

A bowl is formed by revolving the lower half of the ellipse x^2 + 4(y − 1)^2 = 4 around the y-axis. (Repeat: around the Y axis.) Water is then poured in to the bowl up to a depth of 0.75 units. THEN a lead sphere of diameter 1 unit is dropped in the bowl and settles to the bottom. Does the water overflow the bowl when the sphere is dropped in? You can use a computational aid (Maple of Wolfram Alpha) to calculate integrals, but you have to be clear about what integral(s) you set up and had calculated. This is NOT a yes or no question, your response must be backed up quantitatively and specifically.

Answer 1