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Then the formula for the volume will be: If the function is of the y coordinate and the axis of rotation is the x-axis then the formula becomes: If the function is rotating around the line x = h then the formula becomes: [1]
This formula holds whether or not the cylinder is a right cylinder. [7] This formula may be established by using Cavalieri's principle. A solid elliptic right cylinder with the semi-axes a and b for the base ellipse and height h. In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the ...
The mass of any of the discs is the mass of the sphere multiplied by the ratio of the volume of an infinitely thin disc divided by the volume of a sphere (with constant radius ). The volume of an infinitely thin disc is π R 2 d x {\displaystyle \pi R^{2}\,dx} , or π ( a 2 − x 2 ) d x {\textstyle \pi \left(a^{2}-x^{2}\right)dx} .
A pipe is a tubular section or hollow cylinder, usually but not necessarily of circular cross-section, used mainly to convey substances which can flow — liquids and gases , slurries, powders and masses of small solids. It can also be used for structural applications; a hollow pipe is far stiffer per unit weight than the solid members.
The above formula is for the xy plane passing through the center of mass, which coincides with the geometric center of the cylinder. If the xy plane is at the base of the cylinder, i.e. offset by d = h 2 , {\displaystyle d={\frac {h}{2}},} then by the parallel axis theorem the following formula applies:
Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution.
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While the imploding cylinder equations are fundamentally similar to the general equation for asymmetrical sandwiches, the geometry involved (volume and area within the explosive's hollow shell, and expanding shell of detonation product gases pushing inwards and out) is more complicated, as the equations demonstrate.