Solve pi*10^2*144/360=40pi(cm^2)

$$\pi \times 10 ^ { 2 } \times \frac { 144 } { 360 } = 40 \pi ( cm ^ { 2 } )$$

Solve for c

$$c=\frac{1}{m^{2}}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

$$10^{2}\times \frac{144}{360}=40cm^{2}$$

Calculate 10 to the power of 2 and get 100.

$$100\times \frac{144}{360}=40cm^{2}$$

Reduce the fraction \frac{144}{360} to lowest terms by extracting and canceling out 72.

$$100\times \frac{2}{5}=40cm^{2}$$

Multiply 100 and \frac{2}{5} to get 40.

$$40=40cm^{2}$$

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

$$40cm^{2}=40$$

The equation is in standard form.

$$40m^{2}c=40$$

Divide both sides by 40m^{2}.

$$\frac{40m^{2}c}{40m^{2}}=\frac{40}{40m^{2}}$$

Dividing by 40m^{2} undoes the multiplication by 40m^{2}.

$$c=\frac{40}{40m^{2}}$$

Divide 40 by 40m^{2}.

$$c=\frac{1}{m^{2}}$$

Solve for m

$$m=\frac{1}{\sqrt{c}}$$

$$m=-\frac{1}{\sqrt{c}}\text{, }c>0$$