Equation of plane question?

An analytical geometry of three dimensions question?

• My question deals with Plane, solid, and analytical geometry/ Analytical Geometry of three dimensions. I know that the equation of a sphere is: x^2 + y^2 + z^2 - 1 = 0 How about the other Platonic solids? I mean, how could I write an equation for the other solids. For example: rectangular prism. I know that Volume = width × depth × height V = wdh How can I write up a polynomial to represent this geometrical figure? And, if I need to find the derivative of V = wdh, then I write V' = w' *d*h + w*d' *h + w*d*h'

• Answer:

  hmmm, rectangular prism. the lateral faces would be rectangles and the bases would be rectangular as well I gather: I think the formula goes: altitude x base area so think about it practically; all a polynomial is, is an algebraic equation expressed in a particular format if say the bases were squares, you could express the volume as a polynomial as follows base area x height h(constant height)s(side of square)^2 I'm not 100% sure, so don't take me at my word.