Answer to Question #199355 in Calculus for Ben

Question #199355

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


Circular Disk Method:

  1. R:y=√π‘₯, 𝑦=4, π‘¦βˆ’π‘Žπ‘₯𝑖𝑠 axis of revolution: 𝑦=4
  2. 𝑅:𝑦=π‘₯^2, π‘₯=3, π‘₯βˆ’π‘Žπ‘₯𝑖𝑠 axis of revolution: π‘₯=3

Circular Ring Method:

  1. 𝑅: 𝑦=π‘₯^2, 𝑦=2π‘₯ axis of revolution: π‘₯βˆ’π‘Žπ‘₯𝑖𝑠
  2. 𝑅:𝑦^2=4π‘₯, π‘₯^2=4𝑦 axis of revolution: π‘₯=4

Cylindrical Shell Method:

  1. 𝑅:𝑦=π‘₯^2, 𝑦=2π‘₯ axis of revolution: π‘₯βˆ’π‘Žπ‘₯𝑖𝑠
  2. 𝑅: first-quadrant region bounded by 𝑦=4π‘₯ and π‘₯^3=𝑦 axis of revolution: π‘₯=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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