Evaluate v(r)=4/3pir^3

$v (r) = \frac{4}{3} π r^{3}$

Step 1

Remove parentheses.

$v r = \frac{4}{3} \cdot π r^{3}$

Step 2

Divide each term in $v r = \frac{4}{3} \cdot (π r^{3})$ by $r$ and simplify.

Divide each term in $v r = \frac{4}{3} \cdot (π r^{3})$ by $r$ .

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

Simplify the left side.

Cancel the common factor of $r$ .

Cancel the common factor.

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

Divide $v$ by $1$ .

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

Simplify the right side.

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

Factor $r$ out of $\frac{4}{3} \cdot (π r^{3})$ .

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

Cancel the common factors.

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

$v = \frac{r (\frac{4}{3} \cdot (π r^{2}))}{r^{1}}$

Factor $r$ out of $r^{1}$ .

$v = \frac{r (\frac{4}{3} \cdot (π r^{2}))}{r \cdot 1}$

Cancel the common factor.

$v = \frac{r (\frac{4}{3} \cdot (π r^{2}))}{r \cdot 1}$

Rewrite the expression.

$v = \frac{\frac{4}{3} \cdot (π r^{2})}{1}$

Divide $\frac{4}{3} \cdot (π r^{2})$ by $1$ .

$v = \frac{4}{3} \cdot (π r^{2})$

Multiply $\frac{4}{3} (π r^{2})$ .

Combine $π$ and $\frac{4}{3}$ .

$v = \frac{π \cdot 4}{3} r^{2}$

Combine $\frac{π \cdot 4}{3}$ and $r^{2}$ .

$v = \frac{π \cdot 4 r^{2}}{3}$

Move $4$ to the left of $π$ .

$v = \frac{4 π r^{2}}{3}$