Chapter 1.4, Problem 48PPSE

Solution

To solve the equation $S=2\pi r^2+2\pi rh$ for h .

  $h=\frac{S-2\pi r^2}{2\pi r}$

Given:

The equation, $S=2\pi r^2+2\pi rh$ .

Concept Used:

• The opposite operation of addition is subtraction and the opposite operation of subtraction is addition.
• The opposite operation of multiplication is division and the opposite operation of division is multiplication.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

In order to solve the given equation $S=2\pi r^2+2\pi rh$ for h , isolate the variable on one side by performing the basic algebraic operations as shown below

  $\begin{array}{c}S=2\pi r^2+2\pi rh\\ S-2\pi r^2=2\pi r^2+2\pi rh-2\pi r^2\\ S-2\pi r^2=2\pi rh\\ \frac{S-2\pi r^2}{2\pi r}=\frac{2\pi rh}{2\pi r}\\ \frac{S-2\pi r^2}{2\pi r}=h\end{array}$

Thus, the required formula is $h=\frac{S-2\pi r^2}{2\pi r}$ .