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

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

Solve for h (complex solution)

$$\left\{\begin{matrix}\\h=\frac{32r}{3}\text{, }&\text{unconditionally}\\h\in \mathrm{C}\text{, }&r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

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

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

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

Calculate 2 to the power of 3 and get 8.

$$r^{2}h=\frac{4}{3}\times 8r^{3}$$

Multiply \frac{4}{3} and 8 to get \frac{32}{3}.

$$r^{2}h=\frac{32}{3}r^{3}$$

The equation is in standard form.

$$r^{2}h=\frac{32r^{3}}{3}$$

Divide both sides by r^{2}.

$$\frac{r^{2}h}{r^{2}}=\frac{32r^{3}}{3r^{2}}$$

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

$$h=\frac{32r^{3}}{3r^{2}}$$

Divide \frac{32r^{3}}{3} by r^{2}.

$$h=\frac{32r}{3}$$

Solve for h

$$\left\{\begin{matrix}\\h=\frac{32r}{3}\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

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

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

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

Calculate 2 to the power of 3 and get 8.

$$r^{2}h=\frac{4}{3}\times 8r^{3}$$

Multiply \frac{4}{3} and 8 to get \frac{32}{3}.

$$r^{2}h=\frac{32}{3}r^{3}$$

The equation is in standard form.

$$r^{2}h=\frac{32r^{3}}{3}$$

Divide both sides by r^{2}.

$$\frac{r^{2}h}{r^{2}}=\frac{32r^{3}}{3r^{2}}$$

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

$$h=\frac{32r^{3}}{3r^{2}}$$

Divide \frac{32r^{3}}{3} by r^{2}.

$$h=\frac{32r}{3}$$

Solve for r

$$r=0$$

$$r=\frac{3h}{32}$$