Need help C2 Differentiation Question! Watch

jordanwu
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A do it yourself enthusiast wants to buy a square sheet of metal from which to make a square–based, open–topped water tank. The four corner-pieces will be cut away and not used. The rest of the metal will be used to form the five faces of the tank. The tank is to have a capacity of 2 m^3.

Show that when the base of the tank has sides of length x metres, the sides of the sheet of metal must be of length L metres, where

L= x + 4/x^2

Please help! Thanks.
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SH0405
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(Original post by jordanwu)
A do it yourself enthusiast wants to buy a square sheet of metal from which to make a square–based, open–topped water tank. The four corner-pieces will be cut away and not used. The rest of the metal will be used to form the five faces of the tank. The tank is to have a capacity of 2 m^3.

Show that when the base of the tank has sides of length x metres, the sides of the sheet of metal must be of length L metres, where

L= x + 4/x^2

Please help! Thanks.
Ok....so you understand that one can derive the following equation, right?

(x^2)*((L-x)/2)=2

If you rearrange this, it should get you to the correct answer.
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somegirlcalledea
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I did it slightly differently to above poster:

I said that the height of tank was variable h. Therefore x*x*h=2.
I rearranged this to work out h.

Then you can use this to work out L!
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