A cuboid (Rectangular prism has dimension x metres wide, h metres high and 4x metres long. The cuboid is made of 640m of wire.'?
- Wayne DeguManLv 71 month ago
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))
- billrussell42Lv 71 month ago
what is the question?
- davidLv 71 month ago
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.