6. (8 pts) A paper cup has the shape of an inverted circular cone with a diameter of 3 inches and a height of 4 inches. The water cooler dispenses at a rate of 50 cubic inches per minute. (a) How long will it take to fill the cup to the brim? (b) At what rate is the water level rising when the water is a half inch from the top? Note: the volume of a right cone is given by $V = \frac{1}{3}\pi r^2h$. 7. (4 pts) Verify the volume of the cup in the previous problem by recognizing the solid (the filled cup) as a revolution and subsequently using techniques from chapter 6. If instead you develop the volume formula provided, you will received double credit.
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The formula for the volume of a right cone is V = (1/3)πr^2h, where r is the radius and h is the height. In this case, the diameter of the cup is 3 inches, so the radius (r) is 1.5 inches and the height (h) is 4 inches. Show more…
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