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What is surface to volume ratio?

Gramps,
What is surface to volume ratio?
Kelsie, from Hudson, Florida

Dear Kelsie,
Consider a cube whose sides are of length (x). The area of the surface of one side of the cube will be x2, and the area of all six sides would be 6×2. The volume of the cube would be equal to the height times the length times the width, or x3. The surface to volume ratio would be the surface area of the cube divided by its volume, or S/V = 6×2/x3 = 6/x. Thus the surface of a cube is equal to six times the volume of the cube divided by the length of one side, as S = 6V/x. So the larger the cube, the smaller would be the surface to volume ratio.
Consider now a sphere whose surface area would be S = 4 Pi r2, and whose volume would be
V = (4 Pi r3)/3. So the surface of a sphere is equal to the three times volume of the sphere divided by its radius, as S = 3V/r.
Gramps

 
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