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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. 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 flat ...
Pluto's diameter is 2 376.6 ± 3.2 km and its mass is (1.303 ± 0.003) × 10 22 kg, 17.7% that of the Moon (0.22% that of Earth). Its surface area is 1.774 443 × 10 7 km 2, or just slightly bigger than Russia or Antarctica. Its surface gravity is 0.063 g (compared to 1 g for Earth and 0.17 g for the Moon).
- 4.743 km/s
- Clyde W. Tombaugh
- February 18, 1930
- Lowell Observatory
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The sphere has the smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area.
- 2
- O(3)
- 4πr²
The surface area, S, of a right cone is: S = πr 2 + πrl. where r is the radius of the base and l is the slant height. If the height of the cone is given, the surface area is: where h is the height of the right cone. In both these formulas, πr 2 is the area of the base and πrl or is the area of its lateral surface.
Cube. The surface area of a cube is the area of the six squares that cover it. The area of one of them is \ (a \times a,\) or \ (a^2 \). Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared: \ [ (\text {Surface area of cube}) = 6 a^2 .\]
The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: A = 4πr 2 (sphere), where r is the radius of the sphere.
