Basic Math Examples

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\begin{matrix} h = & 11 r = & 6 \end{matrix}

$\begin{array}{r} h = & 11 \\ r = & 6 \end{array}$

Step 1

The volume of a cone is equal to

\frac{1}{3}

$\frac{1}{3}$ times the area of the base

π r^{2}

$π r^{2}$ times the height

h

$h$ .

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

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

Step 2

Substitute the values of the radius

r = 6

$r = 6$ and height

h = 11

$h = 11$ into the formula to find the volume of the cone. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

\frac{1}{3} \cdot π \cdot 6^{2} \cdot 11

$\frac{1}{3} \cdot π \cdot 6^{2} \cdot 11$

Step 3

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 6^{2} \cdot 11

$\frac{π}{3} \cdot 6^{2} \cdot 11$

Step 4

Raise

6

$6$ to the power of

2

$2$ .

\frac{π}{3} \cdot 36 \cdot 11

$\frac{π}{3} \cdot 36 \cdot 11$

Step 5

Cancel the common factor of

3

$3$ .

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Step 5.1

Factor

3

$3$ out of

36

$36$ .

\frac{π}{3} \cdot (3 (12)) \cdot 11

$\frac{π}{3} \cdot (3 (12)) \cdot 11$

Step 5.2

Cancel the common factor.

$\frac{π}{3} \cdot (3 \cdot 12) \cdot 11$

Step 5.3

Rewrite the expression.

$π \cdot 12 \cdot 11$

Step 6

Simplify the expression.

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Step 6.1

Move

$12$ to the left of

$π$ .

$12 \cdot π \cdot 11$

Step 6.2

Multiply

$11$ by

$12$ .

$132 π$

Step 7

The result can be shown in multiple forms.

Exact Form:

$132 π$

Decimal Form:

$414.69023027 \dots$