Solve A=pirsqrt{p+q}

$$A = \pi r \sqrt { p + q }$$

Solve for p

$$\left\{\begin{matrix}p=-q+\left(\frac{A}{\pi r}\right)^{2}\text{, }&\left(A\geq 0\text{ and }r>0\right)\text{ or }\left(A\leq 0\text{ and }r<0\right)\\p\geq -q\text{, }&A=0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\pi r\sqrt{p+q}=A$$

Divide both sides by \pi r.

$$\frac{\pi r\sqrt{p+q}}{\pi r}=\frac{A}{\pi r}$$

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

$$\sqrt{p+q}=\frac{A}{\pi r}$$

Square both sides of the equation.

$$p+q=\frac{A^{2}}{\left(\pi r\right)^{2}}$$

Subtract q from both sides of the equation.

$$p+q-q=\frac{A^{2}}{\left(\pi r\right)^{2}}-q$$

Subtracting q from itself leaves 0.

$$p=\frac{A^{2}}{\left(\pi r\right)^{2}}-q$$

Subtract q from \frac{A^{2}}{\left(\pi r\right)^{2}}.

$$p=-q+\frac{A^{2}}{\left(\pi r\right)^{2}}$$

Solve for A

$$A=\pi \sqrt{p+q}r$$

$$p\geq -q$$