SPHERE 



5495 



SPHINX 



Surface of Sphere. Cut a sphere into two 

 equal parts. Wind a cord about the whole con- 

 vex surface of one of the hemispheres; then 

 wind this same cord about the entire plane 

 surface or base of the hemisphere (which is a 

 great circle of the sphere). You will find that 

 the cord which covered the convex surface 

 will cover the great circle twice. Stated as a 

 rule, this is expressed: The surface of a 

 sphere is equal to the surface of four of its 

 great circles. The area of a circle equals 3.1416, 



Find the weight of a steel ball 20 inches in 

 diameter, steel weighing 480 pounds to the cubio 

 foot. 



Volume of sphere = 



[Explanation appears in text.] 



or TT (pi), times the square of its radius (see 

 CIRCLE). Therefore the surface of any sphere 

 =4 XTTX radius 2 . 



What is the surface of a sphere whose diameter 

 is 12 feet? 



Surface in sq. ft. = 4 X 3.1416 X 62 = 452.3904. 



Volume of Sphere. Take a cylinder of the 

 same diameter as a sphere, and of an altitude 

 equal to the diameter of the sphere. (1) Fill 

 the cylinder with water and in it place the 

 sphere; hold the sphere firmly so that it rests 

 on the base of the cylinder (does not float) 

 and thus displaces its own volume of water. 

 When the sphere is taken out the cylinder is 

 found to be one-third full of water, which 

 shows that the volume of the sphere is two- 

 thirds of the volume of the cylinder. 



(2) Place the sphere in the empty cylinder; 

 fill in with salt, sugar, or sand; take out the 

 sphere, and find that the salt, sugar or sand 

 fills the cylinder to one-third of its height. 



(3) The two solids may be made of clay or 

 putty and weighed, and the relative weights 

 noted. 



All these experiments show that the volume 

 of a sphere is two-thirds the volume of a cyl- 

 inder whose diameter and whose height are 

 each equal to the diameter of the sphere. 



Volume of any cyl indent area of base X height 



Volume of cylinder = irxr2x height 



But in this cylinder the height is equal to 

 diameter or twice the radius (see CYLINDER). 



Volume = TT x r2 x 2r 



Volume = 2 x ir X r 3 

 and 



Volume of sphere = 



Volume of sphere = % x TT X r3 



Volume of sphere = 



The surfaces of spheres are to each other as 

 the squares of their radii. The volumes of 

 spheres are to each other as the cubes of their 

 radii or the cubes of their diameters. The vol- 

 ume of a sphere is, roughly, one-half the vol- 

 ume of a cube whose edge is equal to the 

 diameter of the sphere. A.H. 



SPPIEROID, sfe'roid, a geometrical body re- 

 sembling a sphere, but not perfectly round. 

 In geometry a spheroid is a figure generated by 

 an ellipse revolving about one of its axes. The 

 spheroid is called prolate, or oblong, when it 

 revolves about the longer or major axis of the 

 generating ellipse; when it revolves about its 

 shorter or minor axis it is said to be oblate. 

 The figure of the earth is frequently referred to 

 as an oblate spheroid, as its polar diameter 

 is shorter than its equatorial diameter, and it 

 is somewhat flattened at the poles. A figure 

 generated by any axes of the ellipse other than 

 the major or minor is called a universal sphe- 

 roid. 



SPHINX, sfingks. In Grecian mythology the 

 sphinx was a wicked being usually represented 

 as a lion, having the head of a woman, the tail 

 of a serpent and the wings of a bird. This 

 creature lived in a cliff just outside the cit}' 

 of Thebes, and kept guard over the road to the 

 city. To every passer-by she put this riddle: 

 What animal is it that walks on four legs in 

 the morning, two at noon and three in the 

 evening? And anyone who failed to answer 

 correctly was immediately devoured. When 

 Oedipus passed on the way to Thebes, the rid- 

 dle was put to him, and without much hesita- 

 tion he declared the animal to be man, who 

 walked on his hands and feet when young, 

 erect on his two feet in middle life, and with 

 the aid of a staff in old age. With a howl of 

 rage because her riddle had been read aright, 

 the sphinx hurled herself from the rocks and 

 was killed. 



The Egyptian sphinx was not quite like the 

 Grecian, but had the head of a man and the 

 body, legs, feet and tail of a lion. It had no 

 wings until a later period, when the Greek 

 influence was felt. Originally, the sphinx was 

 supposed to represent the god Horus, guardian 

 of temples and tombs; and when sculptured, 

 the face was probably made to resemble the 

 Pharaoh who ruled at that time. Sometimes 



