Solve 1/3xr^2h=48pi

$$\frac { 1 } { 3 } x r ^ { 2 } h = 48 \pi$$

Solve for h

$$h=\frac{144\pi }{xr^{2}}$$

$$r\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{xr^{2}}{3}h=48\pi$$

Divide both sides by \frac{1}{3}xr^{2}.

$$\frac{3\times \frac{xr^{2}}{3}h}{xr^{2}}=\frac{3\times 48\pi }{xr^{2}}$$

Dividing by \frac{1}{3}xr^{2} undoes the multiplication by \frac{1}{3}xr^{2}.

$$h=\frac{3\times 48\pi }{xr^{2}}$$

Divide 48\pi by \frac{1}{3}xr^{2}.

$$h=\frac{144\pi }{xr^{2}}$$

Solve for r (complex solution)

$$r=-12\sqrt{\pi }h^{-\frac{1}{2}}x^{-\frac{1}{2}}$$

$$r=12\sqrt{\pi }h^{-\frac{1}{2}}x^{-\frac{1}{2}}\text{, }h\neq 0\text{ and }x\neq 0$$

Solve for r

$$r=12\sqrt{\frac{\pi }{hx}}$$

$$r=-12\sqrt{\frac{\pi }{hx}}\text{, }\left(h>0\text{ and }x>0\right)\text{ or }\left(x<0\text{ and }h<0\right)$$