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
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