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Basic Math Examples



\begin{array}{r} r = & \frac{1}{2} \end{array}

$\begin{array}{r} r = & \frac{1}{2} \end{array}$

Step 1

The volume of a sphere is equal to

\frac{4}{3}

$\frac{4}{3}$ times Pi

π

$π$ times the radius cubed.

\frac{4}{3} \cdot π \cdot {(r a d i u s)}^{3}

$\frac{4}{3} \cdot π \cdot {(r a d i u s)}^{3}$

Step 2

Substitute the value of the radius

r = \frac{1}{2}

$r = \frac{1}{2}$ into the formula to find the volume of the sphere. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

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

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

Step 3

Combine fractions.

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Step 3.1

Combine

\frac{4}{3}

$\frac{4}{3}$ and

π

$π$ .

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

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

Step 3.2

Apply the product rule to

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 3.3

Combine.

\frac{4 π \cdot 1^{3}}{3 \cdot 2^{3}}

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

\frac{4 π \cdot 1^{3}}{3 \cdot 2^{3}}

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

Step 4

Simplify the numerator.

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Step 4.1

One to any power is one.

\frac{4 π \cdot 1}{3 \cdot 2^{3}}

$\frac{4 π \cdot 1}{3 \cdot 2^{3}}$

Step 4.2

Multiply

4

$4$ by

1

$1$ .

\frac{4 π}{3 \cdot 2^{3}}

$\frac{4 π}{3 \cdot 2^{3}}$

\frac{4 π}{3 \cdot 2^{3}}

$\frac{4 π}{3 \cdot 2^{3}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Raise

2

$2$ to the power of

3

$3$ .

\frac{4 π}{3 \cdot 8}

$\frac{4 π}{3 \cdot 8}$

Step 5.2

Multiply

3

$3$ by

8

$8$ .

\frac{4 π}{24}

$\frac{4 π}{24}$

Step 5.3

Cancel the common factor of

4

$4$ and

24

$24$ .

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Step 5.3.1

Factor

4

$4$ out of

4 π

$4 π$ .

\frac{4 (π)}{24}

$\frac{4 (π)}{24}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor

4

$4$ out of

24

$24$ .

\frac{4 π}{4 \cdot 6}

$\frac{4 π}{4 \cdot 6}$

Step 5.3.2.2

Cancel the common factor.

\frac{4 π}{4 \cdot 6}

$\frac{4 π}{4 \cdot 6}$

Step 5.3.2.3

Rewrite the expression.

\frac{π}{6}

$\frac{π}{6}$

\frac{π}{6}

$\frac{π}{6}$

\frac{π}{6}

$\frac{π}{6}$

\frac{π}{6}

$\frac{π}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{π}{6}

$\frac{π}{6}$

Decimal Form:

0.52359877 \dots

$0.52359877 \dots$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$