I was asked this question about the volume of a paramecium in my lab class...?

Question

I found the length and width of a paramecium using a microscope with a reticle and micrometer. Now I'm asked to find the volume of the paramecium using my measurements. The directions say to calculate the volume by selecting a formula for some regular shape that corresponds to the paramecium and, using the volume formula for that shape, find the volume of the paramecium. How do you find the volume of any shape without the height? I've thought of only one volume formula that doesn't use height(volume of a circle), but the problem with that one is that I don't know what to use as the radius. Help!

Answer 1

if you think of the paramecium as a rectangle, you have the length and the width. now think about it, if you revolve that rectangle around itself you have a cylinder in 3D. another way to think of it is if you cut a cylinder in half long ways, the cross section will look like rectangle. you have the same length, but the width has now become the diameter of a circle. the diameter lets you find the volume as you multiply the diameter by pi and then multiply by the length (which is now your height!)

Answer 2

" Assume that the cell is a prolate spheroid. Volume = pi (Lw^2/6), where L is length, w is width."
http://www.zoology.ubc.ca/courses/bio332/Labs/GRAZING.HTM

also some very technical measurements of paramecium at http://www.ggause.com/gfg05.htm

"The volume and surface area of a prolate spheroid is:.

volume: 4/3 pi a b^2;"
http://unitmath.com/um/p/Examples/GeometricSolids/GeometricSolids.html

google "prolate spheroid" if you are interested.
or try "volume of football"
http://mathforum.org/library/drmath/view/54665.html