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**rose1** · March 24th 2009, 11:50 AM

How does the surface area of a rectangular prism change if each of the dimensions is doubled?

**masters** · March 24th 2009, 12:45 PM

Originally Posted by rose1

How does the surface area of a rectangular prism change if each of the dimensions is doubled?

Hi rose,

It would increase by a factor of 4.

If the the dimensions of the base are a and b with height c,

$SA_1 = 2ab + 2bc + 2ac$

$SA_1=2(ab+bc+ac)$

Double the dimensions:

$SA_2 = 2(2a \cdot 2b)+2(2b \cdot 2c)+2(2a \cdot 2c)$

$SA_2=8ab+8bc+8ac$

$SA_2=8(ab+bc+ac)$

$SA_2=4(SA_1)$

$SA_2$ is 4 times $SA_1$ .

Example:

Let each edge = 1

$SA_1=2(1 \cdot 1)+2(1 \cdot 1)+2(1 \cdot 1)$

$SA_1 = 6$

Now double the edge to 2

$SA_1=2(2 \cdot 2)+2(2 \cdot 2)+2(2 \cdot 2)$

$SA_2 = 24$

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