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

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

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Answer 1 · 2016-02-29T13:34:04

Divide the Surface Area by the Volume

Explanation:

Dimensions of the rectangular prism

Width = w
Height = h
Length = l

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

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

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

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

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

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