# Eli5 surface to volume ratio?

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Hey all, I’m taking a biology course and am struggling with my professor not explaining things well. We have an exam coming up and she posted a practice exam, the answer key she gave had many incorrect answers on it. This is a question that I challenged; I think the answer is B. Professor maintains that the answer is C, but can not explain it in a way I understand. Aside from the fact that A. and C. are basically the same response, if C is correct, can someone Eli5?

20) Your throat is dry, and you want the last cough drop in the box to last a long time in your mouth. What should you do?

A) Break the cough drop into little pieces and put them all in your mouth. Since each little piece must be dissolved separately, the drop will last longer.

B) Keep the cough drop whole. This maintains the largest surface-to-volume ratio and slows the dissolution of the cough drop.

C) Break the cough drop into little pieces and put them all in your mouth. This decreases the surface-to-volume ratio and slows the dissolution of the cough drop.

D) It doesn’t matter if the cough drop is in one piece or many pieces; the total amount of cough drop is all that matters.

In: 1

The minimum surface-to-volume occurs when you have a sphere.

So if we assume that there is far more saliva than is needed to dissolve the cough drop, all four answers are incorrect.

A is incorrect because the pieces all dissolve at the same time.

B is incorrect because retaining it whole minimizes the surface-to-volume ratio rather than maintains the largest.

C is incorrect because breaking it into pieces maximizes the surface-to-volume ratio rather than decreases it.

D is incorrect because the rate at which the cough drop dissolves is (with our implicit infinite saliva assumption) based on the surface area.