Algebra Examples

$V = \frac{1}{3} π r^{2} h$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (π r^{2} h) = V$ .

$\frac{1}{3} \cdot (π r^{2} h) = V$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{3} π}$ .

$\frac{1}{\frac{1}{3} π} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} V$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{1}{\frac{1}{3} π} (\frac{1}{3} \cdot (π r^{2} h))$ .

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Step 3.1.1.1

Combine $\frac{1}{3}$ and $π$ .

$\frac{1}{\frac{π}{3}} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{3}{π} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.3

Multiply $\frac{3}{π}$ by $1$ .

$\frac{3}{π} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.4

Cancel the common factor of $π$ .

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Step 3.1.1.4.1

Factor $π$ out of $\frac{1}{3} \cdot (π r^{2} h)$ .

$\frac{3}{π} (π (\frac{1}{3} \cdot (r^{2} h))) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.4.2

Cancel the common factor.

$\frac{3}{π} (π (\frac{1}{3} \cdot (r^{2} h))) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.4.3

Rewrite the expression.

$3 (\frac{1}{3} \cdot (r^{2} h)) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.5

Combine $r^{2}$ and $\frac{1}{3}$ .

$3 (\frac{r^{2}}{3} \cdot h) = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.6

Combine $\frac{r^{2}}{3}$ and $h$ .

$3 \frac{r^{2} h}{3} = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.7

Combine $3$ and $\frac{r^{2} h}{3}$ .

$\frac{3 (r^{2} h)}{3} = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.8

Cancel the common factor of $3$ .

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Step 3.1.1.8.1

Cancel the common factor.

$\frac{3 (r^{2} h)}{3} = \frac{1}{\frac{1}{3} π} V$

Step 3.1.1.8.2

Divide $r^{2} h$ by $1$ .

$r^{2} h = \frac{1}{\frac{1}{3} π} V$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{1}{3} π} V$ .

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Step 3.2.1.1

Combine $\frac{1}{3}$ and $π$ .

$r^{2} h = \frac{1}{\frac{π}{3}} V$

Step 3.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$r^{2} h = 1 \frac{3}{π} V$

Step 3.2.1.3

Multiply $\frac{3}{π}$ by $1$ .

$r^{2} h = \frac{3}{π} V$

Step 3.2.1.4

Combine $\frac{3}{π}$ and $V$ .

$r^{2} h = \frac{3 V}{π}$

Step 4

Divide each term in $r^{2} h = \frac{3 V}{π}$ by $r^{2}$ and simplify.

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Step 4.1

Divide each term in $r^{2} h = \frac{3 V}{π}$ by $r^{2}$ .

$\frac{r^{2} h}{r^{2}} = \frac{\frac{3 V}{π}}{r^{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $r^{2}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{r^{2} h}{r^{2}} = \frac{\frac{3 V}{π}}{r^{2}}$

Step 4.2.1.2

Divide $h$ by $1$ .

$h = \frac{\frac{3 V}{π}}{r^{2}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$h = \frac{3 V}{π} \cdot \frac{1}{r^{2}}$

Step 4.3.2

Combine.

$h = \frac{3 V \cdot 1}{π r^{2}}$

Step 4.3.3

Multiply $3$ by $1$ .

$h = \frac{3 V}{π r^{2}}$