Is there a common name for solids where $V = h \cdot A_t = h \cdot A_b$

Question

I'm trying to find a name which describes all solids which have these properties:

• $h = height$
• $A_{t} = top\ area$
• $A_{b} = base\ area$
• $A_{t} = A_{b}$
• $V = h \cdot A_t = h \cdot A_b$

Examples include Prisms, hence Cuboids and Cylinders.

If such a name doesn't exist, what would you call them?

Answer 1

These surfaces are known as generalized cylinders and they show up in differential geometry. The base can be any shape, but there are a few cases that have their own names:

1. A circular cylinder is a cylinder with a circle as its base (This is the normal cylinder).
2. If the base is a ellipse, it respective cylinder would be called an elliptic cylinder.
3. If the base is a parabola, it's known as a parabolic cylinder.
4. If the base is a hyperbola, it's known as a hyperbolic cylinder.

Generalized cylinders can be made over any shape or curve. So under this general definition a cube would be a cylinder with a square base, and a square would be a cylinder with a line as its base. Even a line can be thought of as a cylinder with a single point as its base. Notice that your formulas still hold since the area of a point or line is $0$, so the volume is $0$ as well.