Machinery's Handbook, 31st Edition
SPHERE 55 Sphere.— A sphere is the locus of points equidistant from a given point (the sphere’s cen ter) in three-dimensional space. Similar to the circle, the standard form for the equation of a sphere of radius R and centered at point ( h , k , l ) is: x h – ( ) 2 y k – ( ) 2 z l – ( ) 2 + + R 2 = The general form for the equation of a sphere can be written as follows, where A ≠ 0: Ax 2 Ay 2 Az 2 Bx Cy Dz E + + + + + + = 0 The general and standard forms of the sphere equations are related as follows:
2
2
2
B + + 4 A 2 ---------------- C D
B – 2 A = ----
C – 2 A = ----
D – 2 A = ----
E A – --
=
h
k
l
R
R = radius of sphere D = diameter of sphere N s = total surface area of sphere N v = total volume of sphere
R 1 = radius of outer sphere R 2 = radius of inner sphere G a , K a , S a , T a , U a , W a , Z a = sectional surface areas G v , K v , S v , T v , U v , W v , Z v = sectional volumes
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