Suppose you are drinking root beer from a conical paper cup. the cup has a diameter of 10 centimeters and a depth of 13 centimeters. as you suck on the straw, root beer leaves the cup at the rate of 4 cm3/sec. at what rate is the level of the root beer in the cup changing when the root beer is 10 centimeters deep?

The level of the root beer is dropping at a rate of 0.08603 cm/s.

Explanation:

The volume of the cone is :

Where, V is the volume of the cone

r is the radius of the cone

h is the height of the cone

The ratio of the radius and the height remains constant in overall the cone.

Thus, given that, r = d / 2 = 10 / 2 cm = 5 cm

h = 13 cm

r / h = 5 / 13

r = {5 / 13} h

Also differentiating the expression of volume w.r.t. time as:

Given: = -4 cm³/sec (negative sign to show leaving)

h = 10 cm

So,

The level of the root beer is dropping at a rate of 0.08603 cm/s.

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