SEARCH HOME
Math CentralQuandaries & Queries

search

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,
Penny

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS