If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same, what is the formula to find the modified surface area?

So the question ask to calculate the function or the formula that could be the solution if the width and height of a rectangular prism are shrunk to one seventh and the length stays the same, base on that, I would say that the surface area would be 2 ( 1/7w1/7h + l1/7w + l1/7h)

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rmanquelafquen rmanquelafquen · Answer 2 · 2019-08-21T22:39:06-04:00

Answer:

The answer is \(S_N=\frac{2}{7}*(L*H+L*W+\frac{W*H}{7})\)

Step-by-step explanation:

In order to determine the formula, we have to know the expression of the volume of a rectangular prism.

I have attached an image that shows two formulas about the rectangular prism.

Therefore, using the same notation of the image:

L=length of the rectangular prism

W=width of the rectangular prism

H=height of the rectangular prism

So, the original surface area is:

\(S_o=2*L*H+2*L*W+2*W*H\)

Then, if the width and height of the rectangular prism are each shrunk to one seventh of the original size but the length remains the same, the new surface area is:

\(S_N=2*L*\frac{H}{7}+2*L*\frac{W}{7}+2*\frac{W}{7}*\frac{H}{7}\\S_N=\frac{2}{7}*(L*H+L*W+\frac{W*H}{7})\)

Finally, the formula of the modified surface area is \(S_N\)