The surface area of a solid cylinder is found using the formula $SA = 2\pi r^2 + 2\pi rh$. The volume of a cone is found using the formula $V = \frac{1}{3} \pi r^2 h$. Judy has a solid cylinder whose total surface area is numerically equal to the volume of a particular cone that has a base congruent to the cylinder's base. If the height of both solids is $6$ inches, what is the radius?

wiseowl Aug 25, 2023