EXAMPLES XIV 207 



(41) Find the volume of the surface of revolution formed by 

 that part of the curve y - sin x between x = and x - TC, rotating 

 about the axis of x. 



(42) That part of the line y + 2x - 8 intercepted between the 

 axes of reference rotates about the axes of x and y respectively. 

 Find the volumes of the two cones thus formed. 



(43) That part of the circle x z + y 2 = 25 between x = 1 and x = 5 

 rotates about the axis of x. Find the volume of the zone of the 

 sphere thus produced. 



/ " 77 



(44) That part of the ellipse + u = 1 between x = and x = 5 



5 o 



rotates about the axis of x. Find the volume of the surface of 

 revolution generated. What would be the volume of the surface 

 of revolution generated if the same part of the curve rotates 

 about the axis of y ? 



(45) That part of the curve y = x z 8x + 15 intercepted be- 

 tween the axes of reference, rotates about the axes of x and y 

 respectively. Find the volume of the surface of revolution 

 generated in each case. 



