Solve A=pi(R^2+r^2)

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

Solve for A

$$A=\pi \left(r^{2}+R^{2}\right)$$

Solution Steps

Use the distributive property to multiply \pi by R^{2}+r^{2}.

$$A=\pi R^{2}+\pi r^{2}$$

Solve for R (complex solution)

$$R=-\sqrt{-r^{2}+\frac{A}{\pi }}$$

$$R=\sqrt{-r^{2}+\frac{A}{\pi }}$$

Solve for R

$$R=\sqrt{-r^{2}+\frac{A}{\pi }}$$

$$R=-\sqrt{-r^{2}+\frac{A}{\pi }}\text{, }A\geq \pi r^{2}$$