Question

What is the surface area of a box if it is scaled up by a factor of 10

Answer 1

Answer: 100 x the original surface area of the box.
Discussion: Note that a box implies three dimensions. However, when dealing with surface area, we are dealing only with two dimensions. Therefore, scaling up a box where we have sides a, b, and c, by a factor of 10, we increase each side by a factor of 10. The scaled up box now has each of those dimensions as 10a, 10b, and 10c. Whereas the VOLUME is increased from (a x b x c) to (10a x 10b x 10c), the SURFACE AREA is increased from 2(a x b) + 2(a x c) + 2(b x c) to 2(10a x 10b) + 2(10a x 10c) + 2(10b x 10c). The SURFACE AREA is therefore kept in only square units, while VOLUME is in cubed units.