Graph 1/(x^2), and revolve it around the x axis to form a 'horn' type shape. Prove that the volume is finite, while the area is infinite
no specific equations.. I know that to find the volume you need to use the shell method and take the sum of all the little 'shells'. Also, the area of a cylinder is pi*r*h, but im not sure how to prove that its finite, while the area is infinite.
The Attempt at a Solution
Well like i said, basically I tried to calculate the volume: V = the sum pi(Xi^2-Xi-1^2)(Si-Si^2) where Xi -Xi-1 is the width of the cylinder, and Si-Si^2 is the height. But like i said, thats where i get lost.. Im pretty sure that the answer is going to be something like 1/infinity for the volume and 1/0 for the area..but im not positive.
Any help would be appreciated, Thanks !