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If the material base of 1000 cm2 square box with top open Are provided so you can find

If the data of 1000 square Square centimeters can be used with the base open top Create a box with the box, find the maximum possible volume. Note: The answer to this problem, you input the correct unit Is required.

The dimensions of the base x X x 시키다 m m H and m y = x ^ 2 +4 xy surface so that the x ^ 2 +4 xy = 1000, X, we 2x +4 y to +4 xdy / DX = 0 = has to be differentiated with respect "harness / DX and =- (y and 2x +4) / 4x =- 1/2-y/x volume, V = (x ^ / DX = 2xy and X, we Respect DV + (x ^ 2) Tuna / DX replace the DV / DX a = 2xy + (x ^ 2) (-1/2-y/x 2) y differentiate ) = 2xy - (x ^ 2) / 2 = (x xy is the xy ^ 2) / 2 if the maximum possible volume of the volume DV / DX and = 0 = "xy a - (x ^ 2) / 2 = 0 =" xy a = (x ^ 2) / 2 = "y and = x / 2, so, X a ^ 2 +4 xy a = 1000 = "x ^ 2 +4 x (x / 2) = 1000 =" x ^ 2 +2 x ^ 2 = 1000 = "3 times ^ 2 = 1000 =" x ^ 2 = 333.333 = "x = 18.2574meters y and = x / 2 = 9.1287meters So, the maximum possible volume = 18.2574 * 18.2574 * 9.1287 = 3042.89 m3

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