Question 1097092
<br>If the heights of the cylinder and cone are same and the volumes are the same, then the cone will have the larger radius.  So let r (little r) be the radius of the cylinder, and let R (big r) be the radius of the cone.<br>
The volume of the cone is
{{{(1/3)(pi)(R^2)(10)}}}<br>
The volume of the cylinder is
{{{(pi)(r^2)(10)}}}<br>
Since the volumes are equal,
{{{(1/3)(pi)(R^2)(10) = (pi)(r^2)(10)}}}
{{{(1/3)R^2 = r^2}}}
{{{1/3 = r^2/R^2}}}
{{{sqrt(1/3) = r/R}}}<br>
The ratio of the cylinder radius to the cone radius is
{{{sqrt(1/3) = 1/sqrt(3) = sqrt(3)/3}}}