Question

What is the surface area of a sphere whose great circle has an area of 30 square yards

Answer 1

Check the picture below.

`\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=30 \end{cases}\implies 30=\pi r^2\implies \boxed{\cfrac{30}{\pi }=r^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a sphere}\\\\ A=4\pi r^2\qquad \qquad A=4\pi \left( \boxed{\cfrac{30}{\pi }}\right)\implies A=120`