Solve 10000cm^2=2pi(25)^2+2pi(25)h

$$10000 cm ^ { 2 } = 2 \pi ( 25 ) ^ { 2 } + 2 \pi ( 25 ) h$$

Solve for c

$$\left\{\begin{matrix}c=\frac{\pi \left(h+25\right)}{200m^{2}}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&h=-25\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 25 to the power of 2 and get 625.

$$10000cm^{2}=2\pi \times 625+2\pi \times 25h$$

Multiply 2 and 625 to get 1250.

$$10000cm^{2}=1250\pi +2\pi \times 25h$$

Multiply 2 and 25 to get 50.

$$10000cm^{2}=1250\pi +50\pi h$$

The equation is in standard form.

$$10000m^{2}c=50\pi h+1250\pi$$

Divide both sides by 10000m^{2}.

$$\frac{10000m^{2}c}{10000m^{2}}=\frac{50\pi \left(h+25\right)}{10000m^{2}}$$

Dividing by 10000m^{2} undoes the multiplication by 10000m^{2}.

$$c=\frac{50\pi \left(h+25\right)}{10000m^{2}}$$

Divide 50\pi \left(25+h\right) by 10000m^{2}.

$$c=\frac{\pi \left(h+25\right)}{200m^{2}}$$

Solve for h

$$h=\frac{200cm^{2}}{\pi }-25$$

Steps for Solving Linear Equation

Calculate 25 to the power of 2 and get 625.

$$10000cm^{2}=2\pi \times 625+2\pi \times 25h$$

Multiply 2 and 625 to get 1250.

$$10000cm^{2}=1250\pi +2\pi \times 25h$$

Multiply 2 and 25 to get 50.

$$10000cm^{2}=1250\pi +50\pi h$$

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

$$1250\pi +50\pi h=10000cm^{2}$$

Subtract 1250\pi from both sides.

$$50\pi h=10000cm^{2}-1250\pi$$

Divide both sides by 50\pi .

$$\frac{50\pi h}{50\pi }=\frac{10000cm^{2}-1250\pi }{50\pi }$$

Dividing by 50\pi undoes the multiplication by 50\pi .

$$h=\frac{10000cm^{2}-1250\pi }{50\pi }$$

Divide 10000cm^{2}-1250\pi by 50\pi .

$$h=\frac{200cm^{2}}{\pi }-25$$