Solve 4/3*pi*r^3=1/3*pi*(3r)^2*h

$$\frac { 4 } { 3 } \times \pi \times r ^ { 3 } = \frac { 1 } { 3 } \times \pi \times ( 3 r ) ^ { 2 } \times h$$

Solve for h

$$\left\{\begin{matrix}\\h=\frac{4r}{9}\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

$$\frac{4}{3}r^{3}=\frac{1}{3}\times \left(3r\right)^{2}h$$

Expand \left(3r\right)^{2}.

$$\frac{4}{3}r^{3}=\frac{1}{3}\times 3^{2}r^{2}h$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4}{3}r^{3}=\frac{1}{3}\times 9r^{2}h$$

Multiply \frac{1}{3} and 9 to get 3.

$$\frac{4}{3}r^{3}=3r^{2}h$$

Swap sides so that all variable terms are on the left hand side.

$$3r^{2}h=\frac{4}{3}r^{3}$$

The equation is in standard form.

$$3r^{2}h=\frac{4r^{3}}{3}$$

Divide both sides by 3r^{2}.

$$\frac{3r^{2}h}{3r^{2}}=\frac{4r^{3}}{3\times 3r^{2}}$$

Dividing by 3r^{2} undoes the multiplication by 3r^{2}.

$$h=\frac{4r^{3}}{3\times 3r^{2}}$$

Divide \frac{4r^{3}}{3} by 3r^{2}.

$$h=\frac{4r}{9}$$

Solve for r

$$r=0$$

$$r=\frac{9h}{4}$$