Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 10 centimeters and a depth of 11 centimeters. As you suck on the straw, root beer leaves the cup at the rate of 6 cm3/sec. At what rate is the level of the root beer in the cup changing when the root beer is 8 centimeters deep?The rate the root beer depth is dropping is (minus)  cm/sec.

Question
Asked Oct 2, 2019
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Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 10 centimeters and a depth of 11 centimeters. As you suck on the straw, root beer leaves the cup at the rate of 6 cm3/sec. At what rate is the level of the root beer in the cup changing when the root beer is 8 centimeters deep?

The rate the root beer depth is dropping is (minus)  cm/sec.

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Expert Answer

Step 1

From the given information, the radius of the cone is 5 centimeters and height(depth) of the cone is 11 centimeters.

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1 The formula for volume of the cone is V 3

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Step 2

Find the relation between r and h.

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h 11 11r 5h 5 -h r = 11 The volume of the cone becomes 2 1 V = 3 5 -hh 11 5 -л - πh 33

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Step 3

Differentiate with respect to ...

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d5 dt33 dV dt dh 5 п(3r): dt 33 -6 dh 5 -6 = dt 11

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Math

Calculus