SOLUTION: Find the volume of the solid generated by revolving about the indicated axis the region bounded by y=x , y=1 and x=0. a. The x-axis and using vertical rectangular element or str

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Question 1141851: Find the volume of the solid generated by revolving about the indicated axis the region bounded by y=x , y=1 and x=0.
a. The x-axis and using vertical rectangular element or strip.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
This volume is the difference


      the volume of the cylinder of the radius  r= 1  and the height  h= 1


          MINUS


      the volume of the cone with the base radius  r= 1  and the height  h= 1.


So, the requested volume is  pi%2Ar%5E2%2Ah - %281%2F3%29%2Api%2Ar%5E2%2Ah = %282%2F3%29%2Api%2Ar%5E2%2Ah = %282%2F3%29%2Api%2A1%5E2%2A1 = %282%2F3%29%2Api = %282%2F3%29%2A3.14 = 2.093 cubic units.