# How do you find ratio of surface area to volume in a rectangular prism?

Feb 29, 2016

Divide the Surface Area by the Volume

#### Explanation:

Dimensions of the rectangular prism

Width = w
Height = h
Length = l

surface area (S) = $2 \cdot h \cdot l + 2 \cdot h \cdot w + 2 \cdot l \cdot w$

volume (V) = $h \cdot l \cdot w$

Surface area to volume ratio = $\frac{S}{V}$ = $\frac{2 \left(h \cdot l + h \cdot w + l \cdot w\right)}{h \cdot l \cdot w}$

For a prism of width 2, length 2 and height 4
Surface area would be $2 \cdot \left(4 + 8 + 8\right)$ = $40$
Volume would be $2 \cdot 2 \cdot 4$ = $16$
$\frac{40}{16} = 2.5$
The Surface area to Volume ratio would be 2.5