# Calculating radius as a function of volume and as a function of time

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• Jan 14th 2010, 04:39 PM
surffan
Calculating radius as a function of volume and as a function of time
A gas tank on a dock has a small puncture and is leaking gas at a rate of 1 cm^3/min into a lake. it forms a circular slick that is 1mm thick on the surface of the water.
a) find the amount of gas leaked as a function of time.
b) State the radius of the slick as a function of its volume.
c) State the radius of the slick as a function of time.
d) what is the radius of the slick after 40 minutes?

I'm having trouble figuring out how to approach this question,even if someone can give me a guideline or help me with part of it i'm sure i could figure out the rest based on that. Thank you :)
• Jan 14th 2010, 06:59 PM
skeeter
Quote:

Originally Posted by surffan
A gas tank on a dock has a small puncture and is leaking gas at a rate of 1 cm^3/min into a lake. it forms a circular slick that is 1mm thick on the surface of the water.
a) find the amount of gas leaked as a function of time.
b) State the radius of the slick as a function of its volume.
c) State the radius of the slick as a function of time.
d) what is the radius of the slick after 40 minutes?

I'm having trouble figuring out how to approach this question,even if someone can give me a guideline or help me with part of it i'm sure i could figure out the rest based on that. Thank you :)

(a) volume of gas in $cm^3$ = (leak rate in $cm^3/min$)(time in minutes)

(b) the slick forms a cylindrical shape where $h$ is the thickness ...

$V = \pi r^2 h$ , solve for $r$

(c) work it out using what you found in (a) and (b)

(d) use your time function
• Jan 14th 2010, 09:57 PM
surffan
Thank you so much! I really appreciate it :)