242 PRACTICAL MATHEMATICS 



For the whole cone 

 L 



L OY 



1 f ft , , 



111 I /V)4 fill 



7C//I' I \JU U/U 



2 Jo 

 = 1 R 4 p _ 



2 ft 4 J 



[ (h-yYJ 



5 



2/i 4 

 TimR 4 



= 



Q 



= MR 2 , where M is the mass of the cone. 



Moment of inertia of the slice about the axis AB = - -runx* 8y 



4 



Moment of inertia of the slice about the axis OX = - mx* Sw 



4 



For the whole cone 



Tim f 71 f h 



I ox = - x 4 dy + -urn xhf dy 



* Jo Jo 



I 



Jo 



TrmR 4 f*.. . . , TrmR 2 f A 



I //i 1/1^ fit I ~\- .^ ^^_ I 



J-. I I ft / 1 U/M ^^ , ~ 



4-tl JQ "Jo 



TimR 4 h*_ TtmR 8 ^ 

 1F~ * 5" H ~P~~ X 30 



TzmR 2 h 



10 



3 ,_ /R 2 ^ 2 \ 



-fo M \T + ?) 



131. The Sphere. Considering an elementary slice of thickness 

 &y, situated at a distance y from a horizontal plane passing 

 through the centre of the sphere. 



