# You're reading: Posts Tagged: 3D geometry

### GeoGebra in 3D: ThreeoGebra!

GeoGebra, the Aperiodical’s official Favourite Thing for Messing About With Geometry, has just bumped up to version 5. With that bigger number comes another dimension – GeoGebra now supports three-dimensional geometry!

The formula for the surface area of a sphere, $A=4\pi r^{2}$, is the derivative of the formula for the volume of a sphere: $V=\frac{4}{3}\pi r^{3}$.
This result does not hold for a cube with side length $a$ if the surface area and volume are written in terms of $a$. However, if the surface area and volume are written in terms of half the side length, $r=\frac{a}{2}$, you get the surface area $A=24 r^{2}$, which is the derivative of the volume, $V=8 r^{3}$.