Solve 2piR^2H=27pir^2(10)

$$2 \pi R ^ { 2 } H = 27 \pi r ^ { 2 } ( 10 )$$

Solve for H

$$\left\{\begin{matrix}H=135\times \left(\frac{r}{R}\right)^{2}\text{, }&R\neq 0\\H\in \mathrm{R}\text{, }&r=0\text{ and }R=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

$$2R^{2}H=27r^{2}\times 10$$

Multiply 27 and 10 to get 270.

$$2R^{2}H=270r^{2}$$

Divide both sides by 2R^{2}.

$$\frac{2R^{2}H}{2R^{2}}=\frac{270r^{2}}{2R^{2}}$$

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

$$H=\frac{270r^{2}}{2R^{2}}$$

Divide 270r^{2} by 2R^{2}.

$$H=\frac{135r^{2}}{R^{2}}$$

Solve for R

$$\left\{\begin{matrix}R=3\sqrt{\frac{15}{H}}r\text{; }R=-3\sqrt{\frac{15}{H}}r\text{, }&H>0\\R=0\text{, }&r=0\text{ and }H\neq 0\\R\in \mathrm{R}\text{, }&r=0\text{ and }H=0\end{matrix}\right.$$