NUMBERS AND MEASURES. 



(5) MENSURATION. 



v = 3-1415926536 - = Q'3183098862. 



vr 



TT = 9-8696044 vT= 1 "7724539. 



7T 3 = 31-0061763 ^ - 1-4645919. 



Lengths of Curves. 



1. Circle, radius r L 2wr 



2. Ellipse, axes 2a 2b (approximate) L ir*J2(a 2 + b z ) ? 



(a and b nearly equal). 



Plane Areas. 

 1. Square, side a A = a?. 



% 2. Triangle, base c, perpendicular d A -cd. 



Zt 



3. Rectangle, sides a b A ab. 



4. Circle, radius r A = irr 2 . 



5. Ellipse, axes 2a 2b A = irab. 



Surface*. 



1. Cube, edge a S 6a 2 . 



2. Sphere, radius r S = 4-Trr 2 . 



3. Cylinder, radius r height h S = 2irr(h + r), 



4. Spherical segment, radius r height h S = 2irrh. 



5. Cone, slant height I radius r S irr(l + r). 



Volumes. 



1 . Cube, edge a V a 3 . 



2. Rectangular parallelepiped, edges a b c V abc. 



3. Sphere, radius r V irr 3 . 



o 



4. Spheroid, radii abb V --rrab^. 



o 



5. Cylinder or prism V area of base X 



height. 



6. Cone or pyramid V = - area of base 



o ,. 



x height. 



