QuestionMarta solves $S=2 \pi r h+2 \pi r^{2}$ for $h$ . What is the correct expression for $h$ ?

Studdy Solution

STEP 1

Assumptions1. The given equation is $= \pi r h+ \pi r^{}$ . We are solving for $h$

STEP 2

First, we need to isolate the term with $h$ on one side of the equation. To do this, we subtract $2 \pi r^{2}$ from both sides of the equation.
$-2 \pi r^{2} =2 \pi r h$

STEP 3

Next, to solve for $h$ , we need to divide both sides of the equation by $2 \pi r$ .
$\frac{ -2 \pi r^{2}}{2 \pi r} = h$ This is the solution for $h$ in terms of $$, $r$, and $\pi$. However, none of the given options match this exact form. We can simplify this expression further.

STEP 4

We can divide the numerator in the fraction on the left side of the equation by $2 \pi r$ .
$h = \frac{}{2 \pi r} - r$ This is the simplified form of the equation for $h$ . Comparing this with the given options, we see that it matches the first option.
So, Marta should get $\frac{}{2 \pi r} - r = h$ as the result. END

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