When do we use 2 π vs using π in finding the volume of a region?I've seen that sometimes finding the integral volume of a rotated shape in the xy-plane is multiplied by 2 π, and other times it is only multiplied by π. Can someone please tell me the difference?

Question

When do we use   2  π vs using   π in finding the volume of a region?I&#039;ve seen that sometimes finding the integral volume of a rotated shape in the xy-plane is multiplied by   2  π, and other times it is only multiplied by   π. Can someone please tell me the difference?

Steven Bates · Accepted Answer

Step 1Whether to use   π or   2  π depends on the choice of the two common integration methods.1) If the disk-of-circles method is used, disk area   π      r    2   is applied. The integration is then over a stack of disks,  V  =      ∫    a    b    π      x    2    d  xStep 22) If the shell-of-cylinders method is used, cylinder circumference   2  π  r is applied. The integration is then through cylinder walls,   V  =      ∫    a    b    2  π  x  y  (  x  )  d  x

When do we use 2pi vs using pi in finding the volume of a region?

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