Question

You have one cell that is 1 mm cubed, and another that is 2 mm cubed. You place both into a hypertonic solution. Which will shrivel the most? Explain and use calculations to justify the answer.

Answer 1

(note: p = pi, just didn't want to re-write this in equation mode)

SA/vol = 4pr^2/(4/3*p*r^3) = 4/(4/3) * 1/r = 3/r

Vol=2 2=4pr^2 r=sqrt(1/(2p))
Vol=1 1=4pr^2 r=sqrt(1/p)

The one with the bigger Volume will have a bigger radius and hence a smaller surface area/volume ratio (see first equation). This will mean that diffusion will occur more slowly than the smaller cell (assuming that they are sphere's) so the smaller cell will shrivel the most.

Not sure if this is what your teacher will want but I hope it makes sense :)