Posted by **unknown** on Friday, October 28, 2011 at 10:50am.

Jan says if you double each of the dimensions of a rectangular box, it will take twice as much wrapping paper to wrap it. How do you respond?

- math -
**Jai**, Friday, October 28, 2011 at 11:03am
the surface area of a rectangular solid is given by

SA = 2(LW + LH + WH)

where

W = width, L = length, H = height

if we double all the dimensions,

SA' = 2[(2L)(2W) + (2L)(2H) + (2W)(2H)]

SA' = 2[4LW + 4LH + 4WH]

SA' = 2*4[LW + LH + WH]

SA' = 4*SA

therefore, what Jan says is wrong. It takes 4 times as much wrapping paper to wrap it.

hope this helps~ :)

- math -
**Steve**, Friday, October 28, 2011 at 12:01pm
Since area is 2-dimensional, doubling each linear dimension scales the area by 2^{2} = 4

It changes the volume by 2^{3} = 8

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