MathDB

Three spheres each of unit radius have centers

P,Q,R

with the property that the center of each sphere lies on the surface of the other two spheres. Let

C

denote the cylinder with cross-section

PQR

(the triangular lamina with vertices

P,Q,R

) and axis perpendicular to

PQR

. Let

M

denote the space which is common to the three spheres and the cylinder

C

, and suppose the mass density of

M

at a given point is the distance of the point from

PQR

. Determine the mass of

M

Problem Statement