Parametric Equation of Surfaces

The implicitplot3d gives very unsatisfactory plots of surfaces given in implicit form f(x,y,z)=c. Far nicer plots are obtained by using the plot3d command if one has parametric forms of these surfaces i.e. . This lab asks you to construct parametric representations of some surfaces.

1. 1. Find the parametric representation of the plane x+y+z=1. What range of your parameters represents the part of this plane lying in the first octant.
   2. Without using implicitplot3d, plot the solid bounded by the planes .
2. 1. Find the parametric representation of the cylinders and .
   2. Plot these two cylinders drawing them with different colors. Adjust the parameter ranges to get as nice a picture as possible of the solid consisting of the part of the cylinder lying inside .
3. 1. Using cylindrical coordinates, find the parametric representations of the cone and the hemisphere , .
   2. Use Maple, to draw the solid, inside the sphere , below , above z=0.

 
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