clamtrox said:On the cone surface, ρ and z are related through ρ+z=1. This is the defining equation for that surface. 0 to 1 would define a cylinder, which is equally wide in top and bottom.
The formula for finding the volume of a cone using cylindrical polar coordinates is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
To convert cylindrical polar coordinates (r, θ, z) to Cartesian coordinates (x, y, z), you can use the following equations:
x = rcosθ
y = rsinθ
z = z
Yes, the volume of a cone can be found using only polar coordinates. The formula for finding the volume using polar coordinates is V = (1/3)πr^2h, where r is the distance from the origin to the point on the base and h is the height of the cone.
The height of a cone can be found using the formula h = z/r, where z is the vertical distance from the base to the apex of the cone and r is the distance from the origin to the point on the base.
Yes, cylindrical polar coordinates can be used to find the volume of a cone with a slanted base. The formula for finding the volume would be V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone measured along the slant.