subject: Surface Area To Volume Ratio [print this page] Introduction on surface area to volume ratio:
The surface-area-to-volume ratio also called the surface-to-volume ratio and variously denoted sa/vol or SA:V, is the amount of surface area per unit volume of an object or collection of objects. The surface area to volume ratio is measured in units of inverse distance. A cube with sides of length a will have a surface area of 6a2 and a volume of a3. (Source - wikipedia)
The surface to volume ratio for a cube is thus 6/a. Here we are going to see the formulas for surface area and volume of some regular shapes. Examples to calculate the surface area to volume ratio is given in the following sections.
Formula for Surface Area and Volume:
The formula for the surface area and volume of some regular shapes is given below,
Cube:
Surface area = 6 a2
Volume = a3
Sphere:
Surface area = 4'pi' a2
Volume = '(4pia^3)/3'
Rectangular solid:
Surface area = 2(lw) + 2(lh) + 2(hw)
Volume = l*w*h
Examples to Calculate the Sa/v Ratio:
Here are few examples explaining on how to calculate the surface area to volume ratio,
Example 1:
Find the surface area to volume ratio of a cube with side length = 4cm.
Solution:
Cube:
Surface area = 6 a2
Volume = a3
Surface area = 6 (4*4)
= 6(16)
= 96 cm2
Volume = 4*4*4
= 64 cm3
Surface area to volume ratio = (96/64) cm-1
Ratio = '3/2'
Example 2:
Find the surface area to volume ratio of a rectangular solid with side length = 4cm, width 2 cm and height 2 cm
Solution:
Rectangular solid:
Surface area = 2(lw) + 2(lh) + 2(hw)
Volume = l*w*h
Surface area = 2 [(4*2) + (4*2) +(2*2)]
= 2[ 8 + 8 + 4]
= 2[ 20 ]
= 40 cm2
Volume = 4*2*4
= 32 cm3
Surface area to volume ratio = (40/32) cm-1
Ratio = '5/4'
Example 3:
Find the surface area to volume ratio of a sphere with radius = 4cm.
Solution:
The ratio = '3/a'
=' 3/4' cm-1
In involving a solid material, the surface-area-to-volume is an important factor for the reactivity, that is, the rate at which the chemical reaction will proceed. Materials with large surface area to volume ratios (e.g., very small diameter, or very porous or otherwise not compact) react at much faster rates than monolithic materials, because more surface is available to react. Examples include grain dust; while grain is not typically flammable, grain dust is explosive. Finely ground salt dissolves much more quickly than coarse salt. It is same-case-applicable to a multiparticulate system or any system that has a surface coating, a very important parameter to be consider while performing coating for pharmaceutical solid oral-dosage form.
High surface-area-to-volume ratio provides a strong "driving force" to speed up thermodynamic processes that minimize thermodynamic free energy.
The ratio between the surface area and volume of cells and organisms has an enormous impact on their biology. For example, many aquatic microorganisms have increased surface area to increase their drag in the water. This reduces their rate of sink and allows them to remain near the surface with less energy expenditure. Humans and other large animals cannot rely on diffusion for absorption and ejection of respiratory gases for their whole body; however, animals such as flatworms and leeches can, as they have more surface area per unit volume. For similar reasons, surface to volume ratio places a maximum limit on the size of a cell.
An increased surface area to volume ratio also means increased exposure to the environment. The many tentacles of jellyfish and anemones provide increased surface area for the acquisition of food. Greater surface area allows more of the surrounding water to be sifted for nutrients.
