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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 surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m −1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
For example, a cube with a side length of 1 meter has a surface area of 6 m 2 and a volume of 1 m 3. If the sides of the cube were multiplied by 2, its surface area would be multiplied by the square of 2 and become 24 m 2. Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to ...
The curved surface area of the spherical segment bounded by two parallel disks is the difference of surface areas of their respective spherical caps. For a sphere of radius r {\displaystyle r} , and caps with heights h 1 {\displaystyle h_{1}} and h 2 {\displaystyle h_{2}} , the area is
Divide every face of the cube into nine squares in a similar manner to a Rubik's Cube. This sub-divides the cube into 27 smaller cubes. Remove the smaller cube in the middle of each face, and remove the smaller cube in the center of the larger cube, leaving 20 smaller cubes. This is a level-1 Menger sponge (resembling a void cube).
Scratches, represented by triangular-shaped grooves, make the surface area greater. 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).
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long. [ 1 ] [ 2 ] The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units. [ 3 ]
In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry . The theory is simplified by working in projective space rather than affine space , and so cubic surfaces are generally considered in projective 3-space P 3 ...
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