A right circular cone has a volume of \(\dfrac{1}{9}\pi \) cubic feet and a height of 3 feet. What is the radius, in feet, of the base of the cone?

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The volume formula of a right circular cone is:

$$ V=\frac{1}{3}\pi r^2h $$

Substituting our values for volume and height:

$$ \frac{1}{9}\pi=\frac{1}{3}\pi r^2 (3) $$ $$ \frac{1}{9}=r^2 $$ $$ r=\frac{1}{3} $$