Add Maths Help Please?

Question

I have additional mathematics project work? Can anyone help me please? I think it has something to do with differentiation. Anyway, here's the question:
Company X manufactures cylindrical aluminium tins. The manager plans to reduce the cost of produciton. The production cost is proportional to the area of the aluminium sheet used. The volume each tin holds is 1000cm³ (1 liter)
1. Determine the value of h, r and hence calculate the ratio of h:r when the total surface area of each tin is minimum. Here, h cm denotes the height and r cm the radius of the tin.

2.The top and bottom pieces of the tin of height h cm are cut from square-shaped aluminium sheets. Determine the value for r, h and hence calculate the ratio h:r so that the total area of the aluminium sheets used for making the tin is minimum.

There should be a diagram here to make things clearer for you to understand, so if you need it, just email me.

Thanx so much for the help!!

Answer 1

The area of aluminum used is the area of the sides, 2πrh, plus the area of both ends, 2πr^2.

The volume of the can is V = πr^2h. You can write this as h = V/(πr^2) . The area is then

A = 2πr*(V/πr^2) + 2πr^2 =( 2π^2r^3)/V + 2πr^2

Take the derivative of A with respect to r, and find the minimum for A.
Then solve for h from the equation for volume h = V/(πr^2)

Without a diagram the second part cannot be solved. Obviously the top, bottom and sides are laid out on the square sheet, and you want to minimize the area of the sheet used. Without seeing the pattern, I can't do this. But if you do have the pattern, compute the area of the sheet from the dimensions needed by the can pieces. Then minimize that.

Answer 2

Do your own homework, cheater. You just realized that it's due tomorrow morning?

HAHA!

Answer 3

well it seems like you have to do a quantity * value table