)Unemployed said:
tiny-tim said:Hi Unemployed!
(have a theta: θ and a pi: π and a square-root: √ and try using the X2 icon just above the Reply box
Not for the cone bit
Cylindrical coordinates are a type of coordinate system used to represent points in three-dimensional space. They consist of three components: radius (r), angle (θ), and height (z). These coordinates are commonly used in physics and engineering applications.
To convert from Cartesian coordinates (x, y, z) to cylindrical coordinates (r, θ, z), you can use the following equations:r = √(x² + y²)θ = arctan(y/x)z = z
The volume of a cylinder in cylindrical coordinates is given by V = πr²h, where r is the radius and h is the height. In this case, the height is represented by z, and the radius can be found by setting z=r in the equation z²+y²+x²=4 and solving for r.
In this scenario, the boundaries are given by z=r and z²+y²+x²=4. To find the boundaries for a volume in cylindrical coordinates, you can use the equations r = √(x² + y²) and z = z. These equations will give you the range of values for r and z that will define the boundaries of the volume.
The volume bound by z=r and z²+y²+x²=4 represents a cylinder with a radius of √(4-z²) and a height of z. This can be visualized as a circular disk with varying height along the z-axis. This volume can be useful in applications such as calculating the volume of a cylindrical tank or determining the displacement of a cylindrical object in fluid dynamics.