A cylindrical oatmeal soda can has a capacity of 344 ml. Find the dimensions that will minimize the amount of material needed to construct the container.

r = 3.797 cm

h = 7.594 cm

Step-by-step explanation:

The cylinder volume  V = πr² h

So, given that the volume = 344 ml

Then,

344 = πr² h

Make h the subject of the formula:

 ----- (1)

Similarly, the surface area of a cylinder is expressed by:

A = 2πr² h + 2 πr²   ---- (2)

If we replace the value of h from above in  (1) to (2)

Then;

Taking the differential of A with respect to r, we have:

Set for the minimum surface area.

So,

Divide both sides by 4

r = 3.797 cm

From (1), the height is:

h = 7.594 cm