Calculations at a truncated hollow right circular cone. A truncated hollow cone is a hollow cone with the tip straight cut off within the hollow region, or a truncated cone, of which a smaller, similar truncated cone is removed from its middle. The base is the larger annulus, the top surface is the smaller annulus.
Enter one outer and one inner radius, the thickness or a further radius and the height. Choose the number of decimal places, then click Calculate.
Formulas:
d = R - S = r - s
A = π * [ ( R + r ) * √ (R - r)² + h² + ( S + s ) * √ (S - s)² + h² + ( R² - S² + r² - s² ) ]
V = h * π / 3 * (R² + Rr + r² - S² - Ss - s² )
pi:
π = 3.141592653589793...
Radiuses, thickness and height have the same unit (e.g. meter), the surface has have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
The surface area of a truncated hollow cone is the total surface area of the outer truncated cone, plus the lateral surface area of the inner truncated cone, minus the base and top surface area of the inner truncated cone. Calculating the volume is simpler; it is the volume of the outer truncated cone minus that of the inner truncated cone. The base and top surface areas are two circular rings of different sizes. When viewed from the side, the outline, as with the truncated cone, is an isosceles trapezoid.
The truncated hollow cone has an infinite number of planes of symmetry, all of which pass centrally through both bases. It is rotationally symmetric for every angle about the line common to all these planes of symmetry. The truncated hollow cone is therefore a solid of revolution.
A truncated hollow cone is used for example when a narrower tube needs to be connected to a thicker tube. The geometric equivalent of a tube is a cylindrical shell. A funnel also usually has the shape of a truncated hollow cone, often of two different truncated hollow cones put together.
