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Homework 11 - vu(tv2894 Homework 11(Section 3.7 miner(55096...

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vu (tv2894) – Homework 11 (Section 3.7) – miner – (55096) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the rate at which the volume of a sphere is changing with respect to its radius r when r = 3 cm. 1. rate = 8 π cm 3 / cm 2. rate = 32 π cm 3 / cm 3. rate = 36 π cm 3 / cm correct 4. rate = 48 π cm 3 / cm 5. rate = 27 π cm 3 / cm Explanation: For a sphere with radius r its volume = 4 3 πr 3 . Now the rate at which the volume is changing with respect to r is the derivative of volume with respect to r . Thus rate = d dr (volume) = 4 πr 2 . Consequently, when r = 3 cm., rate = 36 π cm 3 / cm . keywords: rate of change, cube, surface area, application 002 10.0 points If a tank holds 2000 gallons of water, and the water can drain from the tank in 40 min- utes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as V = 2000 parenleftbigg 1 - t 40 parenrightbigg 2 .
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