Basic Math Examples

 $\begin{array}{r} h = & 6 \\ r = & 6 \end{array}$

Step 1

The volume of a cone is equal to $\frac{1}{3}$ times the area of the base $π r^{2}$ times the height $h$ .

$\frac{1}{3} \cdot π \cdot {(r a d i u s)}^{2} \cdot (h e i g h t)$

Step 2

Substitute the values of the radius $r = 6$ and height $h = 6$ into the formula to find the volume of the cone. Pi $π$ is approximately equal to $3.14$ .

$\frac{1}{3} \cdot π \cdot 6^{2} \cdot 6$

Step 3

Multiply $6^{2}$ by $6$ by adding the exponents.

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Step 3.1

Move $6$ .

$\frac{1}{3} \cdot π \cdot (6 \cdot 6^{2})$

Step 3.2

Multiply $6$ by $6^{2}$ .

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Step 3.2.1

Raise $6$ to the power of $1$ .

$\frac{1}{3} \cdot π \cdot (6^{1} \cdot 6^{2})$

Step 3.2.2

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

$\frac{1}{3} \cdot π \cdot 6^{1 + 2}$

Step 3.3

Add $1$ and $2$ .

$\frac{1}{3} \cdot π \cdot 6^{3}$

Step 4

Combine $\frac{1}{3}$ and $π$ .

$\frac{π}{3} \cdot 6^{3}$

Step 5

Raise $6$ to the power of $3$ .

$\frac{π}{3} \cdot 216$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Factor $3$ out of $216$ .

$\frac{π}{3} \cdot (3 (72))$

Step 6.2

Cancel the common factor.

$\frac{π}{3} \cdot (3 \cdot 72)$

Step 6.3

Rewrite the expression.

$π \cdot 72$

Step 7

Move $72$ to the left of $π$ .

$72 π$

Step 8

The result can be shown in multiple forms.

Exact Form:

$72 π$

Decimal Form:

$226.19467105 \dots$