Basic Math Examples

$v = \frac{1}{3} \cdot 3.14 \cdot (3 m^{2}) \cdot (12 m)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot 3.14 \cdot (3 m^{2}) \cdot (12 m) = v$ .

$\frac{1}{3} \cdot 3.14 \cdot (3 m^{2}) \cdot (12 m) = v$

Step 2

Simplify.

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Step 2.1

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

$\frac{3.14}{3} \cdot (3 m^{2}) \cdot (12 m) = v$

Step 2.2

Divide $3.14$ by $3$ .

$1.04\overline{6} \cdot (3 m^{2}) \cdot (12 m) = v$

Step 2.3

Multiply $3$ by $1.04\overline{6}$ .

$3.14 \cdot m^{2} \cdot (12 m) = v$

Step 2.4

Multiply $12$ by $3.14$ .

$37.68 \cdot m^{2} \cdot m = v$

Step 2.5

Raise $m$ to the power of $1$ .

$37.68 \cdot (m^{1} m^{2}) = v$

Step 2.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$37.68 \cdot m^{1 + 2} = v$

Step 2.7

Add $1$ and $2$ .

$37.68 \cdot m^{3} = v$

Step 3

Divide each term in $37.68 \cdot m^{3} = v$ by $37.68$ and simplify.

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Step 3.1

Divide each term in $37.68 \cdot m^{3} = v$ by $37.68$ .

$\frac{37.68 \cdot m^{3}}{37.68} = \frac{v}{37.68}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $37.68$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{37.68 \cdot m^{3}}{37.68} = \frac{v}{37.68}$

Step 3.2.1.2

Divide $m^{3}$ by $1$ .

$m^{3} = \frac{v}{37.68}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply by $1$ .

$m^{3} = \frac{1 v}{37.68}$

Step 3.3.2

Factor $37.68$ out of $37.68$ .

$m^{3} = \frac{1 v}{37.68 (1)}$

Step 3.3.3

Separate fractions.

$m^{3} = \frac{1}{37.68} \cdot \frac{v}{1}$

Step 3.3.4

Divide $1$ by $37.68$ .

$m^{3} = 0.02653927 \frac{v}{1}$

Step 3.3.5

Divide $v$ by $1$ .

$m^{3} = 0.02653927 v$

Step 4

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

$m = \sqrt[3]{0.02653927 v}$