Solve r = pi * h ^ 2 * (r + h/3) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$r=\pi h^{2}(r+\frac{h}{3})$$

Solve for r

$r=\frac{\pi h^{3}}{3\left(1-\pi h^{2}\right)}$
$|h|\neq \frac{1}{\sqrt{\pi }}$

Steps for Solving Linear Equation

Use the distributive property to multiply $\pi h^{2}$ by $r+\frac{h}{3}$.

$$r=\pi h^{2}r+\pi h^{2}\times \frac{h}{3}$$

Express $\pi \times \frac{h}{3}$ as a single fraction.

$$r=\pi h^{2}r+\frac{\pi h}{3}h^{2}$$

Express $\frac{\pi h}{3}h^{2}$ as a single fraction.

$$r=\pi h^{2}r+\frac{\pi hh^{2}}{3}$$

Subtract $\pi h^{2}r$ from both sides.

$$r-\pi h^{2}r=\frac{\pi hh^{2}}{3}$$

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$r-\pi h^{2}r=\frac{\pi h^{3}}{3}$$

Multiply both sides of the equation by $3$.

$$3r-3\pi h^{2}r=\pi h^{3}$$

Combine all terms containing $r$.

$$\left(3-3\pi h^{2}\right)r=\pi h^{3}$$

Divide both sides by $3-3\pi h^{2}$.

$$\frac{\left(3-3\pi h^{2}\right)r}{3-3\pi h^{2}}=\frac{\pi h^{3}}{3-3\pi h^{2}}$$

Dividing by $3-3\pi h^{2}$ undoes the multiplication by $3-3\pi h^{2}$.

$$r=\frac{\pi h^{3}}{3-3\pi h^{2}}$$

Divide $\pi h^{3}$ by $3-3\pi h^{2}$.

$$r=\frac{\pi h^{3}}{3\left(1-\pi h^{2}\right)}$$