surface example

3D Ring Valley Surface Graph

A circular valley with a raised center and outside wall.

z = (sqrt(x^2 + y^2) - 3)^2

Quick facts

  • Formula: z = (sqrt(x^2 + y^2) - 3)^2
  • Category: surface
  • Tags: surface, calculus, z=f(x,y)

What this graph represents

The minimum happens where the radius equals 3.

Where it appears in calculus

This is a clear level-set teaching example.

How to use this graph

  1. Rotate the surface by dragging with your mouse or finger
  2. Use the Embed button to copy an <iframe> for your LMS or lesson page
  3. Click PNG to export a classroom-ready image
  4. Click Formula or LaTeX to copy the equation for your notes

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Teacher prompt

Question: Where is the lowest part?

Answer: The lowest part is the circle whose radius is 3.

Related graphs

Explore more surface examples and compare shapes, slices, and contour behavior.

Saddle Surface

z = x^2 - y^2

A saddle surface curves up in one direction and down in the perpendicular direction.

Gaussian Surface

z = exp(-(x^2 + y^2))

A smooth bell-shaped surface centered at the origin.

Elliptic Paraboloid

z = x^2 + y^2

A bowl-shaped surface that opens upward.

Inverted Paraboloid

z = 12 - x^2 - y^2

A dome-shaped surface with a highest point at the center.

Monkey Saddle

z = x^3 - 3*x*y^2

A three-way saddle with three valleys and three ridges.

Sine Wave Surface

z = sin(x) + sin(y)

Two perpendicular sine waves combined into one surface.

Explore more tools

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3D Surface Plotter

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Worksheet Generator

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How to Graph z=f(x,y)

Step-by-step guide for beginners