Basic Math Examples

$201.06 = \frac{1}{3} \cdot 3.14 \cdot r^{2} \cdot 12$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot 3.14 \cdot r^{2} \cdot 12 = 201.06$ .

$\frac{1}{3} \cdot 3.14 \cdot r^{2} \cdot 12 = 201.06$

Step 2

Simplify.

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Step 2.1

Combine $\frac{1}{3}$ and $3.14$ .

$\frac{3.14}{3} \cdot r^{2} \cdot 12 = 201.06$

Step 2.2

Divide $3.14$ by $3$ .

$1.04\overline{6} \cdot r^{2} \cdot 12 = 201.06$

Step 2.3

Multiply $12$ by $1.04\overline{6}$ .

$12.56 \cdot r^{2} = 201.06$

Step 3

Divide each term in $12.56 \cdot r^{2} = 201.06$ by $12.56$ and simplify.

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Step 3.1

Divide each term in $12.56 \cdot r^{2} = 201.06$ by $12.56$ .

$\frac{12.56 \cdot r^{2}}{12.56} = \frac{201.06}{12.56}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12.56$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12.56 \cdot r^{2}}{12.56} = \frac{201.06}{12.56}$

Step 3.2.1.2

Divide $r^{2}$ by $1$ .

$r^{2} = \frac{201.06}{12.56}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $201.06$ by $12.56$ .

$r^{2} = 16.00796178$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$r = \pm \sqrt{16.00796178}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$r = \sqrt{16.00796178}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$r = - \sqrt{16.00796178}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$r = \sqrt{16.00796178}, - \sqrt{16.00796178}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \sqrt{16.00796178}, - \sqrt{16.00796178}$

Decimal Form:

$r = 4.00099509 \dots, - 4.00099509 \dots$