MAXIMA AND MINIMA 128 



Volume of vessel - 



(2) With lid. 



S = surface area of vessel = 2nxy + 2-KX z , where x = radius of 

 base, and y = height. 



Volume of vessel = izx z y 



s 



27U' J 



Then 



Now is a maximum when y- = 

 That is, when - (S - Crer 2 ) = 



u 



Then x = 



' T 



S 



Height of vessel = y = 



_2S /Grc 



~6> S 



Volume of vessel 



77. Example 5. A sector is removed from a circular disc of 

 sheet metal of given radius, and the remainder is formed into a 

 conical vessel. Find the angle of the sector, so that the volume 

 of the conical vessel shall be greatest. 



Let 6 be the angle of the sector ACB. Then 2n - 6 is the 

 angle of the sector which has to be removed. 



Length of arc ACB = R0, where R is the radius of the circular 

 disc. 



