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:
- R:y=√𝑥, 𝑦=4, 𝑦−𝑎𝑥𝑖𝑠 axis of revolution: 𝑦=4
- 𝑅:𝑦=𝑥2, 𝑥=3, 𝑥−𝑎𝑥𝑖𝑠 axis of revolution: 𝑥=3
Circular Ring Method:
- 𝑅: 𝑦=𝑥2, 𝑦=2𝑥 axis of revolution: 𝑥−𝑎𝑥𝑖𝑠
- 𝑅:𝑦2=4𝑥, 𝑥2=4𝑦 axis of revolution: 𝑥=4
Cylindrical Shell Method:
- 𝑅:𝑦=𝑥2, 𝑦=2𝑥 axis of revolution: 𝑥−𝑎𝑥𝑖𝑠
- 𝑅: first-quadrant region bounded by 𝑦=4𝑥 and 𝑥3=𝑦 axis of revolution: 𝑥=2
- 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?
Comments
Leave a comment