- #1
emk
- 3
- 0
Y=x^2, y=0, x=1 ; about x=2
v=pi r^2 T
I tried 0 to 1 intg (x^3-2)^2+2^2 dx, but it wasn't right. Not sure what to do.
v=pi r^2 T
I tried 0 to 1 intg (x^3-2)^2+2^2 dx, but it wasn't right. Not sure what to do.
QuarkCharmer said:It may help to break that thing up into two different integrals. The thing is shaped like a circus tent. That is, a cylinder with a spire on top. The cylinder integration can be done without calculus. Then do the spire part using your books formula (the formula for volume basically) and add the two.
QuarkCharmer's description makes sense to me. The point of the spire is at x=2, the axis of revolution. But the washer method just seems to complicate matters. emk, were you told to use that method here?verty said:I see no spire on top, just an oddly-shaped cylinder.
haruspex said:QuarkCharmer's description makes sense to me. The point of the spire is at x=2, the axis of revolution. But the washer method just seems to complicate matters. emk, were you told to use that method here?
An axis of revolution for washers/disks is an imaginary line around which a circular shape can be rotated to create a three-dimensional object.
The axis of revolution is used to determine the volume and surface area of a washer/disk by providing a reference point for measuring the dimensions of the shape.
A washer is a two-dimensional shape with a hole in the center, while a disk is a three-dimensional object with a circular base and no hole. In washer/disk calculations, the washer is used to find the volume of a solid with a hollow center, and the disk is used to find the volume of a solid with a solid center.
To find the volume of a washer/disk, you first need to find the area of the circular base using the formula A=πr². Then, you subtract the area of the smaller circle (if using a washer) or add the area of the larger circle (if using a disk) to get the area of the shape. Finally, multiply the area by the height of the shape to get the volume.
The axis of revolution for washers/disks is used in various engineering and manufacturing processes, such as creating cylindrical objects like pipes and tubes, calculating the volume of containers like barrels and buckets, and designing gears and pulleys.