Question

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 cm^{3}/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.

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,

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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