[tex]\it \mathcal{A}=4\pi R^2=\pi|_{:\pi} \Rightarrow 4R^2=1|_{:4} \Rightarrow R^2=\dfrac{1}{4} \Rightarrow R=\dfrac{1}{2}\\ \\ \\ \mathcal{V}=\dfrac{4\pi R^3}{3}=\dfrac{4\pi\cdot\Big(\dfrac{1}{2}\Big)^3}{3}=\dfrac{4\pi\cdot\dfrac{1}{8}}{3}=\dfrac{\pi\cdot\dfrac{1}{2}}{3}=\dfrac{\pi}{2\cdot3}=\dfrac{\pi}{6}\ cm^3[/tex]
