Answer:
[tex]\large\boxed{the\ radius\ R=\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
We have
[tex]V=\dfrac{1}{6}\pi[/tex]
Substitute:
[tex]\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi[/tex] divide both sides by π
[tex]\dfrac{4}{3}R^3=\dfrac{1}{6}[/tex] multiply both sides by 3
[tex]3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}[/tex]
[tex]4R^3=\dfrac{1}{2}[/tex] divide both sides by 4
[tex]R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}[/tex]
