Basic Math Examples

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\begin{array}{r} h = & 4 \\ r = & 3 \end{array}

$\begin{array}{r} h = & 4 \\ r = & 3 \end{array}$

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 = 3

$r = 3$ and height

h = 4

$h = 4$ 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 3^{2} \cdot 4

$\frac{1}{3} \cdot π \cdot 3^{2} \cdot 4$

Step 3

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 3^{2} \cdot 4

$\frac{π}{3} \cdot 3^{2} \cdot 4$

Step 4

Cancel the common factor of

3

$3$ .

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Step 4.1

Factor

3

$3$ out of

3^{2}

$3^{2}$ .

\frac{π}{3} \cdot (3 \cdot 3) \cdot 4

$\frac{π}{3} \cdot (3 \cdot 3) \cdot 4$

Step 4.2

Cancel the common factor.

\frac{π}{3} \cdot (3 \cdot 3) \cdot 4

$\frac{π}{3} \cdot (3 \cdot 3) \cdot 4$

Step 4.3

Rewrite the expression.

π \cdot 3 \cdot 4

$π \cdot 3 \cdot 4$

π \cdot 3 \cdot 4

$π \cdot 3 \cdot 4$

Step 5

Simplify the expression.

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Step 5.1

Move

3

$3$ to the left of

π

$π$ .

3 \cdot π \cdot 4

$3 \cdot π \cdot 4$

Step 5.2

Multiply

4

$4$ by

3

$3$ .

12 π

$12 π$

12 π

$12 π$

Step 6

The result can be shown in multiple forms.

Exact Form:

12 π

$12 π$

Decimal Form:

37.69911184 \dots

$37.69911184 \dots$