Pre-Algebra Examples

 $\begin{array}{r} h = & g h \\ r = & g h \end{array}$

Step 1

The volume of a cylinder is equal to the area of the base $π r^{2}$ times the height.

$π \cdot {(r a d i u s)}^{2} \cdot (h e i g h t)$

Step 2

Substitute the values of the radius $r = g h$ and height $h = g h$ into the formula to find the volume of the cylinder. Pi $π$ is approximately equal to $3.14$ .

$π \cdot (g h^{2}) \cdot (g h)$

Step 3

Multiply $g$ by $g$ by adding the exponents.

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Step 3.1

Move $g$ .

$π \cdot (g \cdot g h^{2}) \cdot h$

Step 3.2

Multiply $g$ by $g$ .

$π \cdot (g^{2} h^{2}) \cdot h$

Step 4

Multiply $h^{2}$ by $h$ by adding the exponents.

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Step 4.1

Move $h$ .

$π \cdot (g^{2} (h \cdot h^{2}))$

Step 4.2

Multiply $h$ by $h^{2}$ .

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Step 4.2.1

Raise $h$ to the power of $1$ .

$π \cdot (g^{2} (h^{1} h^{2}))$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$π \cdot (g^{2} h^{1 + 2})$

Step 4.3

Add $1$ and $2$ .

$π \cdot (g^{2} h^{3})$

$π g^{2} h^{3}$