Math CentralQuandaries & Queries


Question from Tina, a student:

A tin can is to have a given capacity. Find the ratio of the height to diameter if the amount of tin ( total surface area) is a minimum.
Answer (1:1)

I did all the steps but then i got confused when my radius was equal to (v/pie) ^ (1/3)
and i plugged that answer back in to my height equation v/pie(r^2) and was very confused on how to simplify my height equation. Please help thank you so much!

Hi Tina,

You said that you got $ r = \left( \frac{V}{\pi}\right)^ {1/3}$ or $r^3 = \frac{V}{\pi}.$ I got $r^3 = \frac{V}{2 \pi}.$ You also have an earlier expression for $h.$ You want the ratio of height to diameter so take your expression for $h$ and divide both sides by $r.$ On the right side you will have an expression involving $r^3$ so substitute for $r^3$ and simplify. Finally divide both sides by 2 since you want the ratio of height to diameter.

Write back if you need more assistance,

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