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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 ...
The area of this rectangle is lw. The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length l and width w, the formula for the area is: [2] A = lw (rectangle). That is, the area of the rectangle is the length multiplied by the width.
Graphs of surface area, A against volume, V of the Platonic solids and a sphere, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times.
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
The surface area of a parallelepiped is the sum of the areas of the bounding parallelograms: ... (also called a rectangular parallelepiped, ...
Three rectangular prisms are each composed of eight unit cubes.A composite cube with a side of 2 has a volume of 8 units 3 but a surface area of only 24 units 2.A rectangular prism two cubes wide, one cube long and four cubes tall has the same volume, but a surface area of 28 units 2.
The volume (V) and surface area (S) of a toroid are given by the following equations, where r is the radius of the circular section, and R is the radius of the overall shape. V = 2 π 2 r 2 R {\displaystyle V=2\pi ^{2}r^{2}R}
For any surface embedded in Euclidean space of dimension 3 or higher, it is possible to measure the length of a curve on the surface, the angle between two curves and the area of a region on the surface. This structure is encoded infinitesimally in a Riemannian metric on the surface through line elements and area elements.