# Math Help - what is the Best diameter and height for a 1 litre tin of paint?

1. ## what is the Best diameter and height for a 1 litre tin of paint?

Hi, my name is bryan.
A problem was put to me to find out what is the best diameter and height of a 1 litre tin of paint
and what is the efficient proportion of diameter to height?

and does this proportion hold for a 5 litre or 10 litre tin of paint?

Looking for help thankyou, bryan

2. Originally Posted by brysarah
Hi, my name is bryan.
A problem was put to me to find out what is the best diameter and height of a 1 litre tin of paint
and what is the efficient proportion of diameter to height?

and does this proportion hold for a 5 litre or 10 litre tin of paint?

Looking for help thankyou, bryan
"best" in what sense??

3. in the sence of what diameter and height would work the best for a 1 litre tin of paint i guess

the question i have been set only said
What is the best diameter and height for a tin that will contrain 1 litres of paint?
what is this efficient proportion of diameter to heigh
and does the proportion hold for a 5 litre or 10 litre tin of paint?

4. Originally Posted by brysarah
in the sence of what diameter and height would work the best for a 1 litre tin of paint i guess

the question i have been set only said
What is the best diameter and height for a tin that will contrain 1 litres of paint?
what is this efficient proportion of diameter to heigh
and does the proportion hold for a 5 litre or 10 litre tin of paint?
what topic in math are you studying exactly? there are infinite solutions to this problem if you drop "best" thingy. and this does not seem to be a question of trigonometry either.

5. Originally Posted by brysarah
in the sence of what diameter and height would work the best for a 1 litre tin of paint i guess

the question i have been set only said
What is the best diameter and height for a tin that will contrain 1 litres of paint?
what is this efficient proportion of diameter to heigh
and does the proportion hold for a 5 litre or 10 litre tin of paint?
My guess is that you want to minimize the surface area. So we know that the volume is

$V=\pi r^2 h \quad S=2\pi r^2+2 \pi r h$

If you plug the first equation into the 2nd you get

$S =2\pi r^2+2\frac{V}{r}$

Can you minimize this expression?

6. i am studying triganometry at this present time
and this was a question my teacher put to me to solve
i didnt understand it myself so i decided to try a math forum

7. Originally Posted by brysarah
i am studying triganometry at this present time
and this was a question my teacher put to me to solve
i didnt understand it myself so i decided to try a math forum
You need to get clarification from your teacher then. In particular, the meaning of 'best'. Until this term has been defined, it is pointless asking other people for help.

8. i think what it is meaning is
you could have a huge container, that only carries 1 litre of paint or u could have a small container that carries 1 litre of paint
meaning what is the best diameter and height to contain 1 litre of paint
and what is the most efficient

9. Originally Posted by brysarah
i think what it is meaning is
you could have a huge container, that only carries 1 litre of paint or u could have a small container that carries 1 litre of paint
meaning what is the best diameter and height to contain 1 litre of paint
and what is the most efficient
Then post #5 has told you exactly what to do (answering the question asked in that post would help things). Which means this is NOT a trigonometry question. Which is why you were told to get clarification from your teacher.