Pre-Algebra Examples

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

Step 1

The volume of a sphere is equal to $\frac{4}{3}$ times Pi $π$ times the radius cubed.

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

Step 2

Substitute the value of the radius $r = \frac{1}{2}$ into the formula to find the volume of the sphere. Pi $π$ is approximately equal to $3.14$ .

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

Step 3

Combine fractions.

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Step 3.1

Combine $\frac{4}{3}$ and $π$ .

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

Step 3.2

Apply the product rule to $\frac{1}{2}$ .

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

Step 3.3

Combine.

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

Step 4

Simplify the numerator.

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Step 4.1

One to any power is one.

$\frac{4 π \cdot 1}{3 \cdot 2^{3}}$

Step 4.2

Multiply $4$ by $1$ .

$\frac{4 π}{3 \cdot 2^{3}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Raise $2$ to the power of $3$ .

$\frac{4 π}{3 \cdot 8}$

Step 5.2

Multiply $3$ by $8$ .

$\frac{4 π}{24}$

Step 5.3

Cancel the common factor of $4$ and $24$ .

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Step 5.3.1

Factor $4$ out of $4 π$ .

$\frac{4 (π)}{24}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $4$ out of $24$ .

$\frac{4 π}{4 \cdot 6}$

Step 5.3.2.2

Cancel the common factor.

$\frac{4 π}{4 \cdot 6}$

Step 5.3.2.3

Rewrite the expression.

$\frac{π}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{6}$

Decimal Form:

$0.52359877 \dots$

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