Applications of Differentiation - Minimising the Cost of a Cylinder

In this video I use differentiation to calculate the dimensions of a cylindrical water tank that minimises the cost of its construction.

First we have to use the given volume of the cylinder to construct a formulae that relates the radius of the tank to its height.

Secondly, we then derive a function that will describe the cost that the tank will be required.

Third, we use the relationship found in step one to create a new expression for the tank's cost however, now it will be in terms of one variable (radius).

Forth, we differentiate the cost function and set it equal to zero and solve for the cylinder's radius.

Finally, we substitute the radius into the relationship derived in step one to calculate the corresponding height of the cylinder.

I hope the video helps :)

Harold