How can the surface area of a rectangular prism change if evey one of the dimensions is increased by a factor ofx? and how can we prove that?

Results 1 to 2 of 2

- Mar 24th 2009, 12:32 PM #1

- Joined
- Feb 2009
- Posts
- 10

- Mar 24th 2009, 12:43 PM #2
If you are going to ask us for help, give your topic a meaningful subject line. "i need help" says nothing about what kind of problem you are having.

Take any rectangular prism. Let the lengths of the sides (width, height, and length) be $\displaystyle u,\,v,$ and $\displaystyle w.$ Then what is the surface area of this prism? It is just the sum of the areas of each face:

$\displaystyle S=2uv+2vw+2uw.$

If you increase each dimension by a factor of $\displaystyle x$, then the new dimensions are $\displaystyle ux,\,vx,$ and $\displaystyle wx.$ So what will the new surface area be? Now compare this to that of the original.