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Solve for the specified variable or expression.$$V=\frac{1}{3} \pi r^{2} h \text { for } h$$
$h$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 4
Formulas
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Harvey Mudd College
Baylor University
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and this problem were given the formula V equals 1/3 ty r squared H. We're being asked to solve it for H. So what that means is, what we're trying to do is isolate h all by itself on one side of the equation. Well, the first thing I know this is I have that fraction. So what I want to do is get rid of it. Well, that fraction of 1/3 means one is getting divided by three. Well, what would be the offices of dividing by three? Well, that would be multiplying by three. So what I'm going to do is I'm gonna multiply both sides on my equation by three. So, on the left hand side of the equation, we have three times V, which is just three V now on the right hand side of the equation, we need to multiply three times 1/3. Well, that's just equal toe one. So, really, those threes essentially just cancel each other. Oh, so are left with Is pie R squared H. Now remember, our goal is to get h all by itself. Well, what's happening? Teach Well, it's getting multiplied by pi r squared. So to get h by itself, We have to do the opposite of multiplying. But by pi r squared well, that would be to divide by pi r squared. So what we're going to do is we're gonna divide both sides of our equation by pi r squared. So let's see what happens. Well, on the left hand side, we have three V divided by pi r squared Well, nothing can be simplified so we're just laugh with three v divided by pi are squid now on the right hand side, we first have pie getting divided by pi Well, that's equal to one So they cancel each other out. We also have our square getting divided by r squared Well, that's also equal to one. So those terms cancel each a burro And you know this all that's left is a tch So now we've got an h all by itself. So what we found is three v divided by pi r squared is equal to eight
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