Question

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

Circular Ring Method:

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

Cylindrical Shell Method:

1. 𝑅:𝑦=𝑥^2, 𝑦=2𝑥 axis of revolution: 𝑥−𝑎𝑥𝑖𝑠
2. 𝑅: first-quadrant region bounded by 𝑦=4𝑥 and 𝑥^3=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?