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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 ...
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.
A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; [3] ... then a frustum becomes a prism ... the lateral surface area is
Where t is the solidification time, V is the volume of the casting, A is the surface area of the casting that contacts the mold, n is a constant, [clarification needed] and B is the mold constant. This relationship can be expressed more simply as: = Where the modulus M is the ratio of the casting's volume to its surface area:
The surface area of a right prism is: +, where B is the area of the base, h the height, and P the base perimeter. The surface area of a right prism whose base is a regular n-sided polygon with side length s, and with height h, is therefore: = +.
Right rhombic prism: it has two rhombic faces and four congruent rectangular faces. Note: the fully rhombic special case, with two rhombic faces and four congruent square faces ( a = b = c ) {\displaystyle (a=b=c)} , has the same name, and the same symmetry group (D 2h , order 8).
The area of the side is known as the lateral area, L. An open cylinder does not include either top or bottom elements, and therefore has surface area (lateral area) = The surface area of the solid right circular cylinder is made up the sum of all three components: top, bottom and side.
A right circular cone and an oblique circular cone Cylinder: Straight parallel sides and a circular or oval cross section A solid elliptic cylinder A right and an oblique circular cylinder Ellipsoid: A surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation