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January 14th, 2011, 07:18 AM   #1
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Surface area and volume

Gas is being pumped into a spherical balloon at the rate of 100 cubic centimeter per min. When the radius is 10 cm, the surface area changed at a rate of ???

ANS - 20 square centimeter per minute

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January 14th, 2011, 08:08 AM   #2
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Re: Surface area and volume

rate of change of volume with respect to time.

rate of change of radius with respect to time.

rate of change of surface area with respect to time (what we want to compute).

Formula for volume of sphere:

Formula for surface area of sphere:

With radius at 10 cm., calculate dr/dt using derivative of formula for volume:



With radius at 10 cm., calculate ds/dt using derivative of formula for surface area:

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January 14th, 2011, 08:18 AM   #3
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Re: Surface area and volume

This should be in calculus not in geometry















substituting 10cm for r we have

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January 14th, 2011, 11:30 AM   #4
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Quote:
Originally Posted by sivela
Since you're giving units, that should be (and similarly for your next line).

should be in greg1313's last line.
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