Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 8 centimeters and a depth of 9 centimeters. As you suck on the straw, root beer leaves the cup at the rate of 7 cm3/sec. At what rate is the level of the root beer in the cup changing when the root beer is 4 centimeters deep?The rate the root beer depth is dropping is (minus)  cm/sec.

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Asked Oct 3, 2019
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Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 8 centimeters and a depth of 9 centimeters. As you suck on the straw, root beer leaves the cup at the rate of 7 cm3/sec. At what rate is the level of the root beer in the cup changing when the root beer is 4 centimeters deep?

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

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Expert Answer

Step 1

We need to calculate the rate of change of level of root beer in the conical cup, dh/dt.

We know that, for a cone with base radius r and height h, volume is given by,

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1 V-5 πrh πr?h 3

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Step 2

Given,

Diameter of cup = 8 cm

So, radius of cup = 8/2 = 4 cm

Height of cup = 9 cm

dV/dt =...

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4h 4 => r= 9 2 1 V 3 h so, 167T h3 V 243 Differentiating both sides with respect to time, dV 167T dh 3h2 243 dt dt dV 16T dh h2 81 dt dt dh 81 dV dt 16Th2 dt dh 81 x 7 16π (4)2 dt dh 0.705 cm/s dt

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Calculus

Derivative

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