S=2πr^2+2πrh
Solve for h

h = [S / (2πr)] - r

It is a case about two-variable linear equations and we have to solve the equation to get the variable h.

Our main plan is to isolate the variable h alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

We can set it to be like this, i.e., just swapping positions on both sides but not changing the signs.

We subtract both sides with .

We divide both sides with

We get the results as follows:

- - - - - - -

Let's check again from the beginning.

For example, r = 2 and h = 3, then we first calculate the value of S by using the initial equation.

Then, we substitute the results of S (with r = 2) into the new equation that we have compiled with h as the subject.

We get the value h = 3 and it means that the equation has been proven.

Notes:

The formula that we discussed above is a formula for calculating the surface area of a closed cylinder.

Keywords: S=2πr^2+2πrh, solve for h, subtract, divide, subject, to isolate the variable h alone, two-variable linear equations

step-by-step explanation: