Expert: Scott A Wilson - 10/12/2009

Question
.  If each dimension of a box is quadrupled, how are the surface area and the volume affected?  

Answer
Each dimension is quadrupled means each dimension, say L, W, and H, become 4L, 4W, ahd 4H.

The surfrace area originally is 2LW + 2LH + 2WH.

It is now 2(4L)(4W) + 2(4L)(4H) + 2(4W)(4H) = 32LW + 32LH + 32WH = 16(2LW + 2LH + 2WH).

What is in the parenthesis is the initial area, so the new area is 16 times as large.



The old volume is LWH and the new volume is (4L)(4W)(4H) = 64LWH.

Since LWH is the old volume, the new volume is 64 times as large as the old volumne.