Problem #79

A standard exercise in problem solving is to find a solid object that casts a circular shadow, a square shadow, and a triangular shadow when viewed from different vantage points. The usual solution is to intersect a cylinder and a prism as shown in the figures below.

The cylinder is a right circular cylinder of radius 1. A cross-section of the prism (perpendicular to its axis) is an isosceles triangle whose base and height are 2. The altitude of the triangle is parallel to the axis of the cylinder and the axis of the cylinder meets the axis of the prism at right angles.

This month's problem is to find the volume and the (total) surface area of this object.