Solid of Revolution Calculator

Calculations at a solid of revolution. This is formed, when a plane curve rotates perpendicularly around an axis. The curve must not cross the axis. If the curve touches the axis, a closed solid of revolution is formed, otherwise it is a toroid. The lateral surface is calculated with Guldinus first theorem, this needs the curve length and the distance of the curve centroid from the axis. The volume is calculated with Guldinus second theorem, this needs the area under the curve and the distance of the area's centroid from the axis. If the curve line at the top and at the bottom has a distance from the axis, but the area touches the axis, so that at the solid of revolution circular areas are formed there, also upper and lower radius must be entered. Lateral surface, surface area and volume will be calculated.

	Curve length (L):
	Radius at curve centroid (R1):
	Area under curve (A):
	Radius at area centroid (R2):
	Radius top (r1):
	Radius bottom (r2):
	Lateral surface (M):
	Surface area (B):
	Volume (V):
	Surface-to-volume ratio (B/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Length and radiuses have the same unit (e.g. meter), the areas 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 above formulas are not particularly complicated. Nevertheless, calculating the surface area and volume of a solid of revolution can sometimes be a very difficult task. The reason for this is that the area centroid and the curve centroid are difficult to find. The area centroids of some bodies can maybe be found in formula collections, but the curve centroids are rarely found there. In order to calculate these two centroids, you have to work with integrals and thus enter the more complex areas of mathematics. If the generating curve is not defined by a single algebraic function but by several, then of course you have to calculate the sections individually. To get the surface, the individual lateral surfaces are then added together and, if necessary, the upper and lower circles are added. For the total volume, the individual volumes of the layers are added together.