Ad
related to: surface area to radiusgenerationgenius.com has been visited by 10K+ users in the past month
- Loved by Teachers
Check out some of the great
feedback from teachers & parents.
- K-8 Standards Alignment
Videos & lessons cover most
of the standards for every state
- K-8 Math Videos & Lessons
Used in 20,000 Schools
Loved by Students & Teachers
- Grades 3-5 Math lessons
Get instant access to hours of fun
standards-based 3-5 videos & more.
- Loved by Teachers
Search results
Results from the WOW.Com Content Network
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 is the surface area of the spherical cap, , r is the radius of the sphere, h is the height of the cap, and; sr is the unit, steradian, sr = rad 2. Because the surface area A of a sphere is 4πr 2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its centre, or that a steradian subtends 1/4π ≈ 0.07958 of a ...
where is the area (of any shape) on the surface of the sphere and is the radius of the sphere. Solid angles are often used in astronomy , physics , and in particular astrophysics . The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance.
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.
Given the surface area of a non-spherical object A, one can calculate its surface area-equivalent radius by setting = or equivalently = For example, a cube of length L has a surface area of . A cube therefore has an surface area-equivalent radius of
The surface area of the sphere satisfies a proportionality equation similar to the one for the volume of a ball: If A n − 1 (r) is the surface area of an (n − 1)-sphere of radius r, then: = (). Applying this to the above integral gives the expression
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: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables is the radius, = is the circumference (the length of any one of its great circles), is the surface area,
Ad
related to: surface area to radiusgenerationgenius.com has been visited by 10K+ users in the past month