124 PRACTICAL MATHEMATICS 



Now the circumference of the base of the conical vessel must 

 be the same as the length of the arc ACB. 



Circumference of base = R0 



R6 

 Radius of base = 



Length of slant side = R 

 Height = 



T7 1 t ' 1 I 



Volume of conical vessel = - 



3 



FIG. 36. 



Now v will be greatest when A/0 4 - z is greatest : that is, when 



6 

 4 - a is a maximum. 



4rc 2 



06 605 



4 is a maximum when 40 3 - z = 

 That is, when 2 = \ 47C 2 



o 



/2 

 or 6 = 2:ry 3 



The angle of the sector = 2;r 



= 1-153 radians or 66 6'. 



