Pre-Algebra Examples



\begin{matrix} h = & 4 r = & 4 \end{matrix}

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

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 = 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 4^{2} \cdot 4

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

Step 3

Multiply

4^{2}

$4^{2}$ by

4

$4$ by adding the exponents.

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Step 3.1

Move

4

$4$ .

\frac{1}{3} \cdot π \cdot (4 \cdot 4^{2})

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

Step 3.2

Multiply

4

$4$ by

4^{2}

$4^{2}$ .

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Step 3.2.1

Raise

4

$4$ to the power of

1

$1$ .

\frac{1}{3} \cdot π \cdot (4^{1} \cdot 4^{2})

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

Step 3.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{1}{3} \cdot π \cdot 4^{1 + 2}

$\frac{1}{3} \cdot π \cdot 4^{1 + 2}$

\frac{1}{3} \cdot π \cdot 4^{1 + 2}

$\frac{1}{3} \cdot π \cdot 4^{1 + 2}$

Step 3.3

Add

1

$1$ and

2

$2$ .

\frac{1}{3} \cdot π \cdot 4^{3}

$\frac{1}{3} \cdot π \cdot 4^{3}$

\frac{1}{3} \cdot π \cdot 4^{3}

$\frac{1}{3} \cdot π \cdot 4^{3}$

Step 4

Combine

\frac{1}{3}

$\frac{1}{3}$ and

π

$π$ .

\frac{π}{3} \cdot 4^{3}

$\frac{π}{3} \cdot 4^{3}$

Step 5

Raise

4

$4$ to the power of

3

$3$ .

\frac{π}{3} \cdot 64

$\frac{π}{3} \cdot 64$

Step 6

Combine

\frac{π}{3}

$\frac{π}{3}$ and

64

$64$ .

\frac{π \cdot 64}{3}

$\frac{π \cdot 64}{3}$

Step 7

Move

64

$64$ to the left of

π

$π$ .

\frac{64 π}{3}

$\frac{64 π}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{64 π}{3}

$\frac{64 π}{3}$

Decimal Form:

67.02064327 \dots

$67.02064327 \dots$