Solve 2pirh+2pir^2=2pir(h+r)

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

Solve for h

$$h\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 2\pi r by h+r.

$$2\pi rh+2\pi r^{2}=2\pi rh+2\pi r^{2}$$

Subtract 2\pi rh from both sides.

$$2\pi rh+2\pi r^{2}-2\pi rh=2\pi r^{2}$$

Combine 2\pi rh and -2\pi rh to get 0.

$$2\pi r^{2}=2\pi r^{2}$$

Cancel out 2\pi on both sides.

$$r^{2}=r^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any h.

$$h\in \mathrm{R}$$

Solve for r

$$r\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 2\pi r by h+r.

$$2\pi rh+2\pi r^{2}=2\pi rh+2\pi r^{2}$$

Subtract 2\pi rh from both sides.

$$2\pi rh+2\pi r^{2}-2\pi rh=2\pi r^{2}$$

Combine 2\pi rh and -2\pi rh to get 0.

$$2\pi r^{2}=2\pi r^{2}$$

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

$$2\pi r^{2}-2\pi r^{2}=0$$

Combine 2\pi r^{2} and -2\pi r^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any r.

$$r\in \mathrm{R}$$