>Solid Figures>Surface Area and Volume of Solid Figures in GeoGebra

Surface Area and Volume of Solid Figures in GeoGebra

You can use GeoGebra to compute the surface area and volume of solid figures by using their coordinates.

GeoGebra Instruction 1

Area of a Polygon in 3D Space

1.

Open Algebra View under

View in

Menu. Note! You can also open 3D Graphics under

View, but be aware that 3D Graphics can make GeoGebra lag.

2.

In an empty row in Algebra View, use the command

Polygon(Point, $\dots$ , Point)

where you replace each Point field with the points of your polygon. Recall that GeoGebra draws line segments between the vertices in the order you list the points, so make sure that you list them in the same direction if your figure is a regular polygon (either clockwise or counterclockwise, not in a random order). You can always open 3D Graphics temporarily to check if your figure is correct.

The number displayed in the row is the area of the corresponding figure.

Now, if you want to find the surface area of a solid figure which consists of polygons (a polyhedron), you can just repeat Item 2 for all the polygons in your figure and sum their areas.

When it comes to volumes, GeoGebra has several built-in commands to draw the most common solid figures. These commands compute the volume as well. Here are the entries for each of them:

The following is a summary of how you can determine the volume of any of the figures in the above list.

GeoGebra Instruction 2

Volume of a Solid Figure

1.: Open Algebra View under View in Menu. Note! You can also open 3D Graphics under View, but be aware that 3D Graphics can make GeoGebra lag.
2.: Draw the solid figure as described in one of the entries in the list above. Make a note of what GeoGebra names the figure.
3.: Use the command

Volume(Object)

where you replace Object with the name of your figure from the previous step.
4.: The volume of the figure will be displayed in Algebra View.

How to Make a Sphere in GeoGebra

Go back