surface example

3D Square Root Dome Graph

The upper half of a sphere-like dome.

z = sqrt(max(0, 16 - x^2 - y^2))

Teacher prompt

Why does the surface stop at a circle?

Outside the circle the square-root input would be negative.

min z 0.00max z 0.0056 samples

What this graph represents

Only points inside the radius produce positive height.

Where it appears in calculus

This teaches domain restrictions for square roots.

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Related graphs

Open another surface page and compare shape, 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.