chrisbaird said:I think you have a typo because z=r does not define a cone.
Unemployed said:Thanks. So the general formula is (rho^2 sin phi drho d-phi d-theta)
z=rho-cos-phi
r=rho-sin-phi
rho cos phi=rho-sin-phi
tan phi=1
So now with the limits rho from 0-2
phi from 0-1 or is it 0-pi/4?
and theta from 0-pi/2
Unemployed said:So phi is 0-pi/4
and theta is also pi/4?
Unemployed said:0 to pi?
LCKurtz said:Sorry. I won't play the guessing game. Draw the dang picture.
Spherical coordinates are a system of representing points in three-dimensional space using a radius, an inclination angle, and an azimuth angle. The radius is the distance from the origin to the point, the inclination angle is the angle between the radius and the z-axis, and the azimuth angle is the angle between the projection of the radius onto the xy-plane and the x-axis.
Spherical coordinates are related to Cartesian coordinates through the following equations:
x = r * sin(θ) * cos(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(θ)
where r is the radius, θ is the inclination angle, and φ is the azimuth angle.
The volume bound by z=r and z^2+y^2+x^2=4 in spherical coordinates is given by the formula V = (2/3) * π * r^3. This can be derived by using the spherical coordinate equations to transform the Cartesian equation into spherical coordinates, and then integrating over the appropriate ranges of the inclination and azimuth angles.
To find the intersection between z=r and z^2+y^2+x^2=4 in spherical coordinates, we can substitute the value of z=r into the Cartesian equation and solve for the corresponding values of θ and φ. This will give us the coordinates of the point(s) where the two surfaces intersect.
Yes, spherical coordinates can be used to represent any point in three-dimensional space. However, they are most commonly used for points that are located at a significant distance from the origin, such as in astronomy or physics applications. For points that are closer to the origin, Cartesian coordinates may be more convenient to use.