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Your friend Satomi is making dinner, and needs a quarter of an onion. Instead of cutting it into quarters she tells you she can cut off a spherical cap, but she's not sure how thick to make it. You determine that the radius of the onion is 3cm. Use integration to determine how thick (h) Satomi should cut the cap. Round your answer to two decimal places. (You may use a calculator / computer to solve a cubic equation.) Here is an illustration of a spherical cap. (Jhmadden, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0) h a - -1 Let R be the region bounded by y = and y = :|: 4. a: a} Let S be the solid obtained by rotating R about the y-axis. Write an integral giving the volume of S. b} Let T be the solid obtained by rotating R about the line y = 3. Write an integral giving the volume of T. e] Without calculating either integral, exp-Iain why T has greater volume than S.