Related Rates Problem

Dazed

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Jun 15, 2005
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A paper cup has the shape of a cone with a height 10 cm and a radius of 3 cm (at the top). If the water is poured into the cup at a rate of 2 cm^3/s, how fast is the water level rising when the water is 5cm deep?
 

tkhunny

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Apr 12, 2005
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Dazed said:
A paper cup has the shape of a cone with a height 10 cm and a radius of 3 cm (at the top). If the water is poured into the cup at a rate of 2 cm^3/s, how fast is the water level rising when the water is 5cm deep?
I guess that would be a Right Circular cone?
The important leap is that the filled portion of the cup is always similar to any other filled portion of the cup. This makes (3/10)*Height = Radius

V = (1/3)*pi*r^2*h

In this problem

V = (1/3)*pi*((3/10)*h)^2*h = (3/100)*pi*h^3

dV = (9/100)*pi*h^2*dh

We are given

dV = 2 cm^3/sec
h = 5 cm

Thus,

2 cm^3/sec = (9/100)*pi*(5 cm)^2*dh

Solve for dh.
 
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