Solve in Terms of the Arbitrary Variable r V=4/3pir^3

$V = \frac{4}{3} π r^{3}$

Step 1

Simplify $\frac{4}{3} \cdot (π r^{3})$ .

Multiply $\frac{4}{3} (π r^{3})$ .

Combine $π$ and $\frac{4}{3}$ .

$V = \frac{π \cdot 4}{3} r^{3}$

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

$V = \frac{π \cdot 4 r^{3}}{3}$

Move $4$ to the left of $π$ .

$V = \frac{4 π r^{3}}{3}$

Step 2

Solve the equation for $π$ .

Simplify $\frac{4}{3} \cdot (π r^{3})$ .

Multiply $\frac{4}{3} (π r^{3})$ .

Combine $π$ and $\frac{4}{3}$ .

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

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

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

Move $4$ to the left of $π$ .

$\frac{4 π r^{3}}{3} = \frac{4 π r^{3}}{3}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$4 π r^{3} = 4 π r^{3}$

Move all terms not containing $`$ to the right side of the equation.

Subtract $4 π r^{3}$ from both sides of the equation.

$0 = 4 π r^{3} - 4 π r^{3}$

Subtract $4 π r^{3}$ from $4 π r^{3}$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true.

Always true