Question 484458: A cuboid of volume 1125cm^3 has length equal to three times the breadth.
(A)- show that the surface area of the cuboid may be expressed as 6x^2+3000/x
(B) - find the dimensions of the cuboid that give the minimum surface area.
I think i have a right, just need to check but i am completely stuck on b, help would be much appreciated.
the breadth is x and the length is 3x.
thanks
Answer by chessace(471)   (Show Source):
You can put this solution on YOUR website! Yes, you are on the right track.
You have surface area as f(x), so to find the min,
differentiate and set to 0.
12x-3000x^-2 = 0
*(1/12)x^2: x^3 - 250 = 0
breath x = 5 cubeRoot(2) cm
L = 15 cubeRoot(2) cm
H = 15/cubeRoot(4) cm
Double check and the product is indeed 1125 cm^3
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