Question

Imagine five cells, each of a different shape and all requiring oxygen. Which of the following would have the most satisfactory oxygen supply? Why?
1.A cube 1mm on a side.
2.A cylinder 1mm long and 0.1 mm in diameter.
3.A cylinder 10 mm long and 0.1 mm in diameter.
4.A flat disk 0.1 mm thick and 1 mm in diameter.
5.A sphere 1 mm in diameter.
but explain why or why not each and every one of the above choices is the best choice or not the best choice

Answer 1

An oxygen supply is directly proportional to the surface area and inversely proportional to the volume. The ratio of these values can be denoted as a “coefficient of oxygen supply” (COS).
For a cube with edge a, the volume V is defined as: V=a³ = 1 mm³;
For a cube with edge a, the surface area A is defined as: A = 6a² = 6 mm²;
COS = 6/1 = 6;
For a cylinder with radius r and height h, the volume is defined as:
V = 3.14 hr² = 3.14×0.0025 = 7.85x10^-3 mm³;
For a cylinder with radius r and height h, the surface area A is defined as:
A = 2×3.14×r×h+2×3.14×r² = 0.105×3.14 = 0.33 mm²;
COS = 0.33/0.00785 = 42;
A flat disc is a cylinder also, h = 0.1mm and r = 0.05; V = 0.00025×3.14 = 7.85×10^-4 mm³;
The surface area is A = 0.015×3.14 = 0.047 mm²;
COS = 0.047/0.000785 = 60;
For a sphere with radius r, the volume is defined as: V = (4/3) ×3.14×r3 = 0.167×3.14 = 0.524 mm³;
For a sphere with radius r, the surface area is defined as A = 4×3.14×r² = 3.14 mm²;
COS = 3.14/0.524 = 6.
The greatest value of COS is of the flat disc, so it would have the best oxygen supply