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For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of the cube, since V = π / 6 d 3, where d is the diameter of the sphere and also the length of a side of the cube and π / 6 ≈ 0.5236.
where SA is the surface area of a sphere and r is the radius. H = 1 2 π 2 r 4 {\displaystyle H={1 \over 2}\pi ^{2}r^{4}} where H is the hypervolume of a 3-sphere and r is the radius.
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
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 r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
The volume of a sphere with radius r is 4 / 3 πr 3. The surface area of a sphere with radius r is 4πr 2. Some of the formulae above are special cases of the volume of the n-dimensional ball and the surface area of its boundary, the (n−1)-dimensional sphere, given below. Apart from circles, there are other curves of constant width.
An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2] V ≈ 4 π r 2 t , {\displaystyle V\approx 4\pi r^{2}t,}
In terms of the spherical angles, ... where ω n−1 is the volume of the (n−1)-sphere. Contraction rule. Another useful identity expresses the ...
If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone aperture angle, i.e., φ is the angle between the rim of the cap and the ...