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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
A portion of the curve x = 2 + cos(z) rotated around the z-axis A torus as a square revolved around an axis parallel to one of its diagonals.. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints). [1]
Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration.To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness δx, or a cylindrical shell of width δx; and then ...
Specific surface area (SSA) is a property of solids defined as the total surface area (SA) of a material per unit mass, [1] (with units of m 2 /kg or m 2 /g). Alternatively, it may be defined as SA per solid or bulk volume [ 2 ] [ 3 ] (units of m 2 /m 3 or m −1 ).
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.
Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times. The surface-area-to-volume ratio or surface-to-volume ratio (denoted as SA:V, SA/V, or sa/vol) is the ratio between surface area and volume of an object or collection of objects.
The number of points accessible is multiplied by the portion of surface area each point represents to calculate the ASA. The choice of the 'probe radius' does have an effect on the observed surface area, as using a smaller probe radius detects more surface details and therefore reports a larger surface.