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Sorry, I have no clue why the computer writes the equations this way but I'm pretty sure when there is a \ like for this exaple question question V=\frac{4}{3}\pi r^3 it is NOT a division sign I got confused on that for a sec so when it shows that before pi it doesn't mean divide by pi, just saying. Sorry for making you go through the trouble, but THANK YOU VERY MUCH for lookin into this and helping out, I really appreciate it!

 

An open cylindrical tank has a volume of 500 cubic feet. The inside surface requires an annual coat of paint. One gallon of paint covers 100 square feet. To the nearest gallon, how many gallons of paint are needed if the tank has been constructed to minimize the coat of paint on the inside surface?

 Dec 8, 2020
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For cylinder, V = pi*r^2*h

A = 2*pi*r*h + 2*pi*r^2

 

dV/dt = pi*r*dr/dt*h + pi*r^2*dh/dt

dA/dt = 2*pi*dr/dt*h + 2*pi*dr/dt*2

 

Plug in V = 500 and A = 100 to get r = 5 and h = 10, so A = 150*pi  ==> 5 gallons of paint

 Dec 9, 2020

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