Question

Determine the surface-area to volume ratio for a rectangular prism with the indicated dimensions. Show all steps 4 x 4 x 3

Answer 1

A prism with dimensions $x\times y\times z$ has volume $xyz$ and surface area $2xy+2yz+2xz$.

So, the surface-area-to-volume ratio is

$\dfrac{2xy+2yz+2xz}{xyz}=\dfrac{2\times4\times4+2\times4\times3+2\times4\times3}{4\times4\times3}=\dfrac{32+24+24}{48}=\dfrac53$