Pre-Algebra Examples

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\begin{matrix} r = & \frac{3}{64} \end{matrix}

$\begin{array}{r} r = & \frac{3}{64} \end{array}$

Step 1

The surface area of a sphere is equal to

4

$4$ times Pi

π

$π$ times the radius squared.

4 π \cdot {(r a d i u s)}^{2}

$4 π \cdot {(r a d i u s)}^{2}$

Step 2

Substitute the value of the radius

r = \frac{3}{64}

$r = \frac{3}{64}$ into the formula to find the surface area of the sphere. Pi

π

$π$ is approximately equal to

3.14

$3.14$ .

4 \cdot π \cdot {(\frac{3}{64})}^{2}

$4 \cdot π \cdot {(\frac{3}{64})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to

\frac{3}{64}

$\frac{3}{64}$ .

4 π \cdot \frac{3^{2}}{64^{2}}

$4 π \cdot \frac{3^{2}}{64^{2}}$

Step 3.2

Raise

3

$3$ to the power of

2

$2$ .

4 π \cdot \frac{9}{64^{2}}

$4 π \cdot \frac{9}{64^{2}}$

Step 3.3

Raise

64

$64$ to the power of

2

$2$ .

4 π \cdot \frac{9}{4096}

$4 π \cdot \frac{9}{4096}$

4 π \cdot \frac{9}{4096}

$4 π \cdot \frac{9}{4096}$

Step 4

Cancel the common factor of

4

$4$ .

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Step 4.1

Factor

4

$4$ out of

4 π

$4 π$ .

4 (π) \cdot \frac{9}{4096}

$4 (π) \cdot \frac{9}{4096}$

Step 4.2

Factor

4

$4$ out of

4096

$4096$ .

4 (π) \cdot \frac{9}{4 (1024)}

$4 (π) \cdot \frac{9}{4 (1024)}$

Step 4.3

Cancel the common factor.

$4 π \cdot \frac{9}{4 \cdot 1024}$

Step 4.4

Rewrite the expression.

$π \cdot \frac{9}{1024}$

$π \cdot \frac{9}{1024}$

Step 5

Combine

$π$ and

$\frac{9}{1024}$ .

$\frac{π \cdot 9}{1024}$

Step 6

Move

$9$ to the left of

$π$ .

$\frac{9 π}{1024}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9 π}{1024}$

Decimal Form:

$0.02761165 \dots$

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