How to Make a Sphere in GeoGebra

GeoGebra is a great tool for visualizing spheres in 3D, and for finding the sphere’s radius and center.

GeoGebra Instruction 1

Drawing a Sphere

1.

Open Algebra View and 3D Graphics under

View in

Menu.

2.

If you know the equation of the sphere, you can type it in Algebra View as it is. The sphere will now appear in Algebra View as an equation. The sphere will also be drawn in 3D Graphics.

If you know the sphere’s radius and center, use the command

Sphere(<point>, <radius>)

where <point> is the center and <radius> is the radius of the sphere. The sphere will now appear in Algebra View as an equation. The sphere will also be drawn in 3D Graphics.

Example 1

I want to draw the sphere given by the equation

{(x - 2)}^{2} + {(y - 1)}^{2} + z^{2} = 64,

which is a sphere with center $(2, 1, 0)$ and radius 8. Following the instructions above, I get the sphere pictured below.

Screenshot of GeoGebra showing a sphere in a three-dimentional coordinate system

GeoGebra Instruction 2

Finding the Radius and Center of a Sphere

1.: Open Algebra View and 3D Graphics under View in Menu.
2.: Enter the equation of the sphere, as given in your exercise. The sphere is now shown in Algebra View as an equation. It’s also displayed as a surface in 3D Graphics.
3.: You get the radius of the sphere by using the command

Radius(<conic>)

where <conic> is the name of the equation in Item 2.
4.: You get the center by using the command

Center(<conic>)

where <conic> is the name of the equation in Item 2.

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