Which coordinate system is a three-dimensional representation of the polar coordinate system?

Which coordinate system is a three-dimensional representation of the polar coordinate system?

• A. Cartesian coordinate system
• B. Cylindrical coordinate system
• C. Spherical coordinate system
• D. Polar coordinate system

Answer: (C)

Extending polar coordinates into three dimensions happens by keeping the same radial distance and angle in the horizontal plane and adding a height component. That yields the cylindrical coordinate system, which uses (r, θ, z): r and θ describe position in the xy-plane as in polar coordinates, and z provides vertical position. Spherical coordinates also describe 3D space with distance and angles, but they do so from the origin with two angles and a radius in a way that’s tied to spheres, not a direct extension of the polar description in the xy-plane. So the natural 3D counterpart to polar is the cylindrical coordinate system.

Extending polar coordinates into three dimensions happens by keeping the same radial distance and angle in the horizontal plane and adding a height component. That yields the cylindrical coordinate system, which uses (r, θ, z): r and θ describe position in the xy-plane as in polar coordinates, and z provides vertical position. Spherical coordinates also describe 3D space with distance and angles, but they do so from the origin with two angles and a radius in a way that’s tied to spheres, not a direct extension of the polar description in the xy-plane. So the natural 3D counterpart to polar is the cylindrical coordinate system.