can anyone please answer this question:

A can is to be made to hold a litre of oil. Find the radius of the can that will minimize the cost of the metal to make the can. (take 1 L= 1000 cm cube)

Printable View

- November 22nd 2005, 03:02 PMmillion_degreezcalculus help
can anyone please answer this question:

A can is to be made to hold a litre of oil. Find the radius of the can that will minimize the cost of the metal to make the can. (take 1 L= 1000 cm cube) - November 22nd 2005, 09:44 PMBubbleBrain_103
we can write the volume of a can (I assume cylindrical) in terms of its height and radius:

pi*r^2*h = V

If our volume is fixed at 1000 cm^3, then for given r, our h is determined.

The surface area of the same cylinder is given by:

A =2*Pi*r*h + 2*pi*r^2

The first term is the area of the cylindrical part of the can, the second term corresponds to the top and bottom disks of the can.

A is the quantity we wish to minimize. From our first equation,

h = V/(pi*r^2), so substitute this into the equation for A:

A(r) = 2*Pi*r*V/(pi*r^2) + 2*pi*r^2

= 2*1000/r + 2*pi*r^2

Now I assume you can use calculus to find the minimum of the function A with respect to the variable r, so finish the job.