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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.
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 ...
Two pi bonds are the maximum that can exist between a given pair of atoms. Quadruple bonds are extremely rare and can be formed only between transition metal atoms, and consist of one sigma bond, two pi bonds and one delta bond. A pi bond is weaker than a sigma bond, but the combination of pi and sigma bond is stronger than either bond by itself.
where V is the volume of a sphere and r is the radius. S A = 4 π r 2 {\displaystyle SA=4\pi r^{2}} where SA is the surface area of a sphere and r is the radius.
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.
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.
There is no more than 1 sigma bond between any two atoms. Molecules with rings have additional sigma bonds, such as benzene rings, which have 6 C−C sigma bonds within the ring for 6 carbon atoms. The anthracene molecule, C 14 H 10, has three rings so that the rule gives the number of sigma bonds as 24 + 3 − 1 = 26. In this case there are 16 ...
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,}