Pre-Algebra Examples

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

Step 1

The surface area of a sphere is equal to $4$ times Pi $π$ times the radius squared.

$4 π \cdot {(r a d i u s)}^{2}$

Step 2

Substitute the value of the radius $r = \frac{3}{64}$ into the formula to find the surface area of the sphere. Pi $π$ is approximately equal to $3.14$ .

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

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{3}{64}$ .

$4 π \cdot \frac{3^{2}}{64^{2}}$

Step 3.2

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

$4 π \cdot \frac{9}{64^{2}}$

Step 3.3

Raise $64$ to the power of $2$ .

$4 π \cdot \frac{9}{4096}$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Factor $4$ out of $4 π$ .

$4 (π) \cdot \frac{9}{4096}$

Step 4.2

Factor $4$ out of $4096$ .

$4 (π) \cdot \frac{9}{4 (1024)}$

Step 4.3

Cancel the common factor.

$4 π \cdot \frac{9}{4 \cdot 1024}$

Step 4.4

Rewrite the expression.

$π \cdot \frac{9}{1024}$

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:

$0.02761165 \dots$