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Volume by disk/washers
- Thread starter Allanr13
- Start date
When the region by the graphs of y=x and y=4x-x^(2) is revolved about the y-axis the volume of the solid generated is given by...
Have you read the post: "Read Before Posting!!"
You should get the idea that we don't "give answers," rather we check your work and give hints.
The first thing you have to do is finish the "..." at the end of the question. Your subject line mentions disks and washers. How would you set up to use that method?
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
No, you don't- Although it would be a good idea to graph the region. Do you know what is meant by "disks and washers" here?Well I think that first i would need to find the area of the region before finding the volume.
1) graph the two functions, y = x and y = 4x - x^2, and shade the area between them.yes, a disk or washer is created when you take the given function(s) and rotate it about the y-axis or x-axis and it becomes a 3D shape
2) find the limits of x and y .. where are the intersection points?
3) when you rotate this figure about the y-axis, do you form a disk, or is it a washer?
4) What is the cross-sectional area as a function of y?
5) What is the incremental volume, dV? What are you going to integrate?
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
- Messages
- 7,763
The point being that each slice has area given by the formula for the area of a circle.yes, a disk or washer is created when you take the given function(s) and rotate it about the y-axis or x-axis and it becomes a 3D shape