Basic Math Examples

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\begin{array}{r} h = & 6 \\ r = & 4 \end{array}

$\begin{array}{r} h = & 6 \\ r = & 4 \end{array}$

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 = 4

$r = 4$ and height

h = 6

$h = 6$ 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 4^{2} \cdot 6

$\frac{1}{3} \cdot π \cdot 4^{2} \cdot 6$

Step 3

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 4^{2} \cdot 6

$\frac{π}{3} \cdot 4^{2} \cdot 6$

Step 4

Raise

4

$4$ to the power of

2

$2$ .

\frac{π}{3} \cdot 16 \cdot 6

$\frac{π}{3} \cdot 16 \cdot 6$

Step 5

Combine

\frac{π}{3}

$\frac{π}{3}$ and

16

$16$ .

\frac{π \cdot 16}{3} \cdot 6

$\frac{π \cdot 16}{3} \cdot 6$

Step 6

Cancel the common factor of

3

$3$ .

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Step 6.1

Factor

3

$3$ out of

6

$6$ .

\frac{π \cdot 16}{3} \cdot (3 (2))

$\frac{π \cdot 16}{3} \cdot (3 (2))$

Step 6.2

Cancel the common factor.

\frac{π \cdot 16}{3} \cdot (3 \cdot 2)

$\frac{π \cdot 16}{3} \cdot (3 \cdot 2)$

Step 6.3

Rewrite the expression.

π \cdot 16 \cdot 2

$π \cdot 16 \cdot 2$

π \cdot 16 \cdot 2

$π \cdot 16 \cdot 2$

Step 7

Simplify the expression.

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Step 7.1

Multiply

2

$2$ by

16

$16$ .

π \cdot 32

$π \cdot 32$

Step 7.2

Move

32

$32$ to the left of

π

$π$ .

32 π

$32 π$

32 π

$32 π$

Step 8

The result can be shown in multiple forms.

Exact Form:

32 π

$32 π$

Decimal Form:

100.53096491 \dots

$100.53096491 \dots$