Hi, Given a rectangular prism and the volume of 800 cubic inches, I have to deri

Question

Hi,

Given a rectangular prism and the volume of 800 cubic inches, I have to derive a function (A(w)) that represents the surface area.

The measurements are unknown but we have H, W, and L which is 4L.

I have H = 800=HW(4W) = H=200/W2 Plugging this into the SA of 2LH+2HW+2LW, I have 2L(200/W2)+2(200/W2)W+2LW and this is where I get lost. If you can help, please list the steps. Thanks!! Hi,

Given a rectangular prism and the volume of 800 cubic inches, I have to derive a function (A(w)) that represents the surface area.

The measurements are unknown but we have H, W, and L which is 4L.

I have H = 800=HW(4W) = H=200/W2 Plugging this into the SA of 2LH+2HW+2LW, I have 2L(200/W2)+2(200/W2)W+2LW and this is where I get lost. If you can help, please list the steps. Thanks!!

Explanation / Answer

given L = 4W H = 200/W^2 W = W thus SA = 2LH+2HW+2LW = 2(4w*200/w^2 + (200/w^2)*w + 4w^2) = 2(800/W + 200/W + 4W^2) = 2(1000/W + 4W^2) A(W) = 2000/W + 8W^2 Ans.

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