Answer to Question #198991 in Calculus for Ben

Question #198991

Find the volume of the solid generated when the region R bounded by the given curves is revolved about the indicated axis, Sketch the Graph.



Circular Disk Method:


  1. R:y=√𝑥, 𝑦=4, 𝑦−𝑎𝑥𝑖𝑠 axis of revolution: 𝑦=4
  2. 𝑅:𝑦=𝑥2, 𝑥=3, 𝑥−𝑎𝑥𝑖𝑠 axis of revolution: 𝑥=3


Circular Ring Method:


  1. 𝑅: 𝑦=𝑥2, 𝑦=2𝑥 axis of revolution: 𝑥−𝑎𝑥𝑖𝑠
  2. 𝑅:𝑦2=4𝑥, 𝑥2=4𝑦 axis of revolution: 𝑥=4


Cylindrical Shell Method:


  1. 𝑅:𝑦=𝑥2, 𝑦=2𝑥 axis of revolution: 𝑥−𝑎𝑥𝑖𝑠
  2. 𝑅: first-quadrant region bounded by 𝑦=4𝑥 and 𝑥3=𝑦 axis of revolution: 𝑥=2
  3. An oil tank in the shape of a sphere has a diameter of 60 ft. How much oil does the tank contain if the depth of the oil is 25ft?
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