how can u change One attribute of a rectangular prisim for volume and for surface area?

Question

how do you change one of the atrributes of a rectangular prisim for surface area and volyume?

Answer 1

If you make the prism longer, volume=cross-section area times length. If A is the cross-section area then the original volume = xA where x is the original length and the new volume is yA where y is the new length. The ratio of the volumes is V₁/V₀=yA/xA=y/x, so you can find the new volume V₁=(y/x)V₀, where V₀ is the original volume.

Surface area (original)=2(xW+xH+WH) where W=width and H=height (unchanged);

new surface area=2(yW+yH+WH), so new/old=(yW+yH+WH)/(xW+xH+WH).

This can be written: (y(W+H)+WH)/(x(W+H)+WH). You need to know W and H or their sum and product to see how the surface area is changed when the third dimension changes from x to y. Note that all 3 dimensions are interchangeable so it doesn't matter what you refer to as length, width and height. W and H simply represent the unchanging dimensions.