Algebra Examples

V = π r^{2} \frac{h}{3}

$V = π r^{2} \frac{h}{3}$

Step 1

Rewrite the equation as

π r^{2} (\frac{h}{3}) = V

$π r^{2} (\frac{h}{3}) = V$ .

π r^{2} (\frac{h}{3}) = V

$π r^{2} (\frac{h}{3}) = V$

Step 2

Multiply

π r^{2} (\frac{h}{3})

$π r^{2} (\frac{h}{3})$ .

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Step 2.1

Combine

π

$π$ and

\frac{h}{3}

$\frac{h}{3}$ .

r^{2} \frac{π h}{3} = V

$r^{2} \frac{π h}{3} = V$

Step 2.2

Combine

r^{2}

$r^{2}$ and

\frac{π h}{3}

$\frac{π h}{3}$ .

\frac{r^{2} (π h)}{3} = V

$\frac{r^{2} (π h)}{3} = V$

\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}

$\frac{3}{π}$ .

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

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

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}

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

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Step 4.1.1.1

Combine.

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

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

Step 4.1.1.2

Cancel the common factor of

3

$3$ .

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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

$1$ .

$h = \frac{3 V}{π r^{2}}$