Posted by **mash** on Monday, December 2, 2013 at 12:25am.

A cylindrical can is made from tin.If it can be contain liquid inside it then what is the parameter of design if we are oblige use the minimum amount of tin.

- calculas,math -
**Steve**, Monday, December 2, 2013 at 5:17am
assuming a constant volume v, we have

v = pi r^2 h

so, h = v/(pi r^2)

the surface area is

a = 2pi r(r+h)

= 2pi r(r + v/(pi r^2))

= 2 pi r^2 + 2v/r

da/dr = 4pi r - 2v/r^2

= 2(2pi r^3 - v)/r^2

we want da/dr=0 for max/min area, so

r = ∛(v/(2pi))

h = v/(pi r^2) = ∛(4v/pi)

but, is this min or max area? Check a'' to be sure it's a minimum

## Answer this Question

## Related Questions

- Math - A cylindrical can is made from tin.If it can be contain 1000 m^3 liquid ...
- Math (Word Problem into formula) - A chemist is studying the properties of a ...
- geometry - A cylindrical tin can holding 2 gal.has its height equal to the ...
- solid mensuration - A cylindrical tin can holding 2 gal.has its height equal to ...
- calculus - Use differentials to estimate the amount of tin in a closed tin can ...
- Chemistry Stoichiometry - 1. Tin and oxygen gas are reacted together to form Tin...
- calculus - right circular cylindrical tin cans are to be manufactured to ...
- math - Maureen fills a cylindrical tin with sugar cookies for a gift. She plans ...
- Chemistry - A compound of Tin Sulfate is decomposed in the lab to give 1.91g of ...
- physics - When a closed tin is heated, the pressure inside it increases. This ...