# A cuboid (Rectangular prism has dimension x metres wide, h metres high and 4x metres long. The cuboid is made of 640m of wire.'?

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• You have not asked an actual question. Given the information in your statement, and the length constraint of 640m, we could go on to say, ''Find the dimensions that maximise the volume''

Length => 4l + 4w + 4h

so, 4(4x) + 4x + 4h

Hence, 640 = 20x + 4h

i.e. h = 160 - 5x

Now, Volume is lwh => 4x²h

so, V = 4x²(160 - 5x) => 640x² - 20x³

Now, dV/dx = 1280x - 60x² = 0 at maximum

i.e. 20x(64 - 3x) = 0

Hence, x = 64/3 => 21.33333 metres

d²V/dx² = 1280 - 120x

With x = 64/3, d²V/dx² < 0.....confirming maximum

Then, h = 160 - 5(64/3) => 160/3 metres

i.e. maximum volume is 4(64/3)²(160 - 5(64/3))

Hence, 97090m³

:)>

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• what is the question?

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• wire length  =  4h  +  4L + 4w

640  =  4h + 4*4x + 4x  >>>  divide by 4

160  =  h + 5x

Something is missing ...  Maybe ypu want max volume? or min Vol.?  or max surface area?  or min surface area?  ...  There is nothing else to do unless tthe question asks one of these questions.

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