SOL 

 SOLIDS the five regular, surface and solidity of. 



SOLIDS, contents of. 



Let x and y be the abscissa and ordinate of any curve j then if * =s 

 3.14159 &c. 



Solid content 



Ex. 1; Content of cylinder = yy*x. 



2. Content of cone = l / 3 x y* x y s of circumscribing cylinder. 



3. Content of paraboloid = % r */ 2 .r ^ circumscribing cylinder. 



4. Content of sphere % of circumscribing cylinder. 



5. Content of spheroid round ax. maj. 



4 ar 5* a . 4 a 8 6 ' 



__ . Do. round ax. mm. . 



o > 



6. Content of pyramid = % content of prism of the same base and alti- 

 tude. 



Guldinus* property. 



I^et M D E K be any plane figure revolving 

 about an axis xy in its own plane, then the 

 solid generated is equal to the circumference 

 described by the centre of gravity multiplied 

 into the area of the figure. 



Ex. Let D M E K be a circle, then the solid 

 will represent the ring of an anchor j in this 

 case if r radius of circle, and a A O, the 

 *olid = 2 * a X 9 r* = 2 ^ ar*. 



