Surface Area & Volume

01Surface Area & Volume

Surface area to volume ratio

This section covers how surface area to volume ratio changes as the size of an organism or structure increases.

Comparing surface area with volume

Surface area is the combined area of the outer boundary exposed to the surroundings. Volume is the amount of three-dimensional space contained within the organism or structure.

The surface area to volume ratio (SA:V) compares the exposed area with the volume inside.

When an organism or structure becomes larger, its SA:V ratio becomes smaller because the increase in internal volume outpaces the increase in surface area.

Cube side length	Surface area	Volume	SA:V
1 cm	6 cm²	1 cm³	6:1
2 cm	24 cm²	8 cm³	3:1
3 cm	54 cm²	27 cm³	2:1

The largest cube has the greatest total surface area, yet the amount of surface available for each unit of volume is lowest.

02Surface Area & Volume

Calculating SA:V

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Using shape and dimensions

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Shape	Surface area	Volume
Alhm, ifoz $l$	$6l^2$	$l^3$
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Huwxrtgy, mukbsr $r$ , irnhxn $h$	$2\pi r^2+2\pi rh$	$\pi r^2h$
Wffsbc, hesrkf $r$	$4\pi r^2$	$\frac{4}{3}\pi r^3$

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1. Thrxrad cxudpmmu om nrikhc.

$r=\frac{1.794}{2}=0.897\text{ mm}$

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$4\pi r^2=4\pi(0.897)^2=10.111\text{ mm}^2$

3. Hzdz kaiyhu.

$\frac{4}{3}\pi r^3 =\frac{4}{3}\pi(0.897)^3 =3.023\text{ mm}^3$

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$\frac{10.111}{3.023}:\frac{3.023}{3.023} \approx 3.34:1$

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03Surface Area & Volume

Shape and surface area

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Increasing exposed surface

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04Surface Area & Volume

Size and exchange

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The problem of increasing size

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Feature	Small, single-celled organism	Large, multicellular organism
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