MathDB

Consider a piece of material in the shape of a right circular conical frustum with radii

R,r,R>r

. A cavity in the shape of another coaxial right circular conical frustum was drilled into the material (see the picture). That way only half of the original volume of material remained. Compute radii

R',r'

of the cavity. Decide for which ratio

R/r

the problem has a solution. https://cdn.artofproblemsolving.com/attachments/b/f/12f579458b7cf0fc31849b319e6f58e50b0363.png

Problem Statement