🚀Related Rates Balloon problem ! ! ! ! ! - vTomb

🚀Related Rates Balloon problem ! ! ! ! !

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RELATED RATES PLAYLIST: https://goo.gl/85bbsG
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In this video you will learn how to find the Rate of Change of Surface Area of the Spherical Balloon given its radius at time t and the Rate of Change of its Volume.

Gas is escaping from a spherical balloon at the rate of 4 cubic feet per minute. How fast is the surface area of the balloon shrinking when the radius of the balloon is 4 feet?

0:26 Using the Sphere Volume formula/equation
0:53 Understanding keywords in the problem
1:51 Understanding Rate of Change - Differentiating the Volume equation implicitly
3:29 Using known quantities in the resulting equation
4:22 Solving for r'(t)
5:08 Using the Surface Area formula/equation
5:17 Differentiating the Surface Area equation implicitly
5:44 Using the found expression for r'(t) in the found differentiated Surface Area equation S'(t) - plugging in known quantities/substitutions to derive S'(t) equation in terms of radius r(t)
6:40 Using the known r(t) to find particular S'(t)

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