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=βπ₯, π¦=4, π¦βππ₯ππ axis of revolution: π¦=4
- π
:π¦=π₯2, π₯=3, π₯βππ₯ππ axis of revolution: π₯=3
Circular Ring Method:
- π
: π¦=π₯2, π¦=2π₯ axis of revolution: π₯βππ₯ππ
- π
:π¦2=4π₯, π₯2=4π¦ axis of revolution: π₯=4
Cylindrical Shell Method:
- π
:π¦=π₯2, π¦=2π₯ axis of revolution: π₯βππ₯ππ
- π
: first-quadrant region bounded by π¦=4π₯ and π₯3=π¦ axis of revolution: π₯=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?
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