## MATHS BITE: Steinmetz Solid

Named after mathematician Charles Proteus Steinmetz, a Steinmetz solid is the solid body generated by the intersection of two or three cylinders with the same radii at right angles.

These solids are named after Steinmetz as he managed to determine the volume of the intersection, though these solids were known long before he studied them.

If two/three cylinders intersect then the intersection is called a bicylinder/tricylinder.

### Bicylinder

Surface Area: 16r2

Volume: , where r is the radius of both cylinders.

The volume of the cube minus the volume of the eight pyramids is the volume of the bicylinder: the volume of 8 pyramids is .

Then the bicylinder volume is:

Surface Area:

Volume:

M x