math
posted by unknown on .
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?

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~ :) 
Since area is 2dimensional, doubling each linear dimension scales the area by 2^{2} = 4
It changes the volume by 2^{3} = 8