Solve each formula for the specified variable. Assume that...

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator.
$$
S=2 \pi r h+2 \pi r^{2}, \text { for } h \quad(\text { surface area of a right circular cylinder })
$$

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Key Concepts

Inverse Operations

Inverse operations are used to ‘undo’ mathematical operations and are crucial when solving equations. For example, if a variable is multiplied by a coefficient, you use division (the inverse operation) to cancel out that multiplication, which is key in isolating the variable. This systematic use of operations helps to simplify and solve linear equations.

Non-Zero Denominator Consideration

When solving equations that involve division or terms in the denominator, it is critical to note any restrictions on the variables such that the denominator is not zero. This ensures that the operations performed are valid and the solution is mathematically acceptable. Such considerations help maintain the integrity of the solution in algebraic manipulations.

Isolation of a Variable

This concept involves rearranging an equation to get the variable of interest by itself on one side of the equation. In algebra, isolating the variable is a fundamental procedure that allows you to express one variable explicitly in terms of others. Techniques such as adding, subtracting, multiplying, or dividing both sides of the equation are used so that the variable you’re solving for stands alone.

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