Question

marta is solving the equation $s = 2\pi rh + 2\pi r^2$ for $h$. which should be the result? $s - \frac{2\pi}{r} = h$; $s - \frac{r}{2\pi} = h$; $\frac{s - r}{2\pi r} = h$; $\frac{s}{2\pi r} - r = h$

Explanation:

Step1: Isolate the term with h

We start with the equation \( S = 2\pi rh+2\pi r^{2} \). First, subtract \( 2\pi r^{2} \) from both sides to get the term with \( h \) alone.
\( S - 2\pi r^{2}=2\pi rh \)

Step2: Solve for h

Now, divide both sides of the equation \( S - 2\pi r^{2}=2\pi rh \) by \( 2\pi r \) to isolate \( h \).
\( h=\frac{S - 2\pi r^{2}}{2\pi r}=\frac{S}{2\pi r}-\frac{2\pi r^{2}}{2\pi r}=\frac{S}{2\pi r}-r \)

Answer:

\(\frac{S}{2\pi r}-r = h\) (the last option: \(\boldsymbol{\frac{S}{2\pi r}-r = h}\))