Algebra Examples

$V = π r^{2} \frac{h}{3}$

Step 1

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

$π r^{2} (\frac{h}{3}) = V$

Step 2

Multiply $π r^{2} (\frac{h}{3})$ .

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Step 2.1

Combine $π$ and $\frac{h}{3}$ .

$r^{2} \frac{π h}{3} = V$

Step 2.2

Combine $r^{2}$ and $\frac{π h}{3}$ .

$\frac{r^{2} (π h)}{3} = V$

$\frac{r^{2} π h}{3} = V$

Step 3

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

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Combine.

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

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Cancel the common factor.

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

Step 4.1.1.2.2

Rewrite the expression.

$\frac{r^{2} π h}{π} = \frac{3}{π} V$

Step 4.1.1.3

Cancel the common factor of $π$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{r^{2} π h}{π} = \frac{3}{π} V$

Step 4.1.1.3.2

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

$r^{2} h = \frac{3}{π} V$

Step 4.2

Simplify the right side.

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Step 4.2.1

Combine $\frac{3}{π}$ and $V$ .

$r^{2} h = \frac{3 V}{π}$

Step 5

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

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Step 5.1

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 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $h$ by $1$ .

$h = \frac{\frac{3 V}{π}}{r^{2}}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 5.3.2

Combine.

$h = \frac{3 V \cdot 1}{π r^{2}}$

Step 5.3.3

Multiply $3$ by $1$ .

$h = \frac{3 V}{π r^{2}}$