Pre-Algebra Examples

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

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 $r = \frac{3}{4}$ into the formula to find the volume of the sphere. Pi $π$ is approximately equal to $3.14$ .

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

Step 3

Combine $\frac{4}{3}$ and $π$ .

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

Step 4

Apply the product rule to $\frac{3}{4}$ .

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

Step 5

Combine.

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

Step 6

Cancel the common factor of $4$ and $4^{3}$ .

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Step 6.1

Factor $4$ out of $4 π \cdot 3^{3}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $3 \cdot 4^{3}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{π \cdot 3^{3}}{3 \cdot 4^{2}}$

Step 7

Cancel the common factor of $3^{3}$ and $3$ .

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Step 7.1

Factor $3$ out of $π \cdot 3^{3}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3 \cdot 4^{2}$ .

$\frac{3 (π \cdot 3^{2})}{3 (4^{2})}$

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{π \cdot 3^{2}}{4^{2}}$

Step 8

Simplify the expression.

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Step 8.1

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

$\frac{π \cdot 9}{4^{2}}$

Step 8.2

Raise $4$ to the power of $2$ .

$\frac{π \cdot 9}{16}$

Step 8.3

Move $9$ to the left of $π$ .

$\frac{9 π}{16}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{9 π}{16}$

Decimal Form:

$1.76714586 \dots$