Basic Math Examples



\begin{matrix} h = & 3 r = & 2 \end{matrix}

$\begin{array}{r} h = & 3 \\ r = & 2 \end{array}$

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 = 2

$r = 2$ and height

h = 3

$h = 3$ 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 2^{2} \cdot 3

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

Step 3

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 2^{2} \cdot 3

$\frac{π}{3} \cdot 2^{2} \cdot 3$

Step 4

Raise

2

$2$ to the power of

2

$2$ .

\frac{π}{3} \cdot 4 \cdot 3

$\frac{π}{3} \cdot 4 \cdot 3$

Step 5

Combine

\frac{π}{3}

$\frac{π}{3}$ and

4

$4$ .

\frac{π \cdot 4}{3} \cdot 3

$\frac{π \cdot 4}{3} \cdot 3$

Step 6

Cancel the common factor of

3

$3$ .

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Step 6.1

Cancel the common factor.

$\frac{π \cdot 4}{3} \cdot 3$

Step 6.2

Rewrite the expression.

$π \cdot 4$

Step 7

Move

$4$ to the left of

$π$ .

$4 π$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 π$

Decimal Form:

$12.56637061 \dots$