Construct the projections of a right square pyramid. The axis of the pyramid lies on the line \(\small o[O_1(1,13,0); P(15,1.5,14.5)]\,\,\), the point \(\small A(6,3,3)\) is a vertex of the base and the height of the pyramid equals \(\small v=9\).
Scheme of spatial solution
\(\small A\in\,\)\(\small\mathrm P\), \(\small o \perp \) \(\small\mathrm P\) \(\small S=o\cap\) \(\small\mathrm P\) \(\small V\in o\), \(\small \,\,d(S,V)=v\) 
Solution via Monge's method (step by step)

Final drawing
Construct the projections of a cube if one edge of the cube lies on the line \(\small p[P_1(3,6,0); P_2(20,0,12)]\) and one vertex that is on the same side as the given edge is the point \(\small A(16,7,4)\).
Scheme of spatial solution
\(\small A\in\) \(\small\mathrm P\), \(\small p \subset \) \(\small\mathrm P\) \(\small D\in p\), \(\small \overline{AD}\perp p\) to the plane \(\small\mathrm P\) \(\small \overline{AE}\perp\,\,\)\(\small\mathrm P\), \(\small \,\,d(A,E)=d(A,D)\) 
Solution via Monge's method (step by step)

Final drawing
Construct the projections of a cone of revolution with the vertex \(\small V(2,10,1)\), the axis lying on the line \(\small o [V, O_1(1,11.5,0)]\), one generatrix lying on the line \(\small i [V, I_1(1,12.5,0)]\) and the radius of the base equal to \(\small r=3.5\).
Scheme of spatial solution
\(\small o\subset \Sigma\), \(\small i\subset \Sigma\) \(\small S\) center of the base \(\small I \) foot of the generatrix \(\small i\) \(\small S\in\) \(\small\mathrm P\), \(\small o \perp \) \(\small\mathrm P\) radius \(\small \overline{SI}\) is the base circle of the given cone. 
Solution via Monge's method (step by step)

Final drawing
Construct the projections of a cone of revolution with given vertex \(\small V(6,14,12)\) whose base lies in the plane \(\small\mathrm P\)\(\small (4,3,5)\) and touches the plane \(\small \Pi_2\).
Scheme of spatial solution
\(\small V\in o\), \(\small o \perp\,\) \(\small\mathrm P\) \(\small S=o\cap\,\)\(\small\mathrm P\) \(\small A\in r_2\), \(\small SA\,\perp\,r_2\) \(\small \overline{SA}\) is the base of the given cone. 
Solution via Monge's method (step by step)

Final drawing
Construct the projections of a cylinder of revolution if the segment \(\small \overline{GH}[G(11,11,4);H(15,13,6)]\) is a chord of one base, the axis lies in the plane \(\small \Gamma(2,1.5,6)\) and the height of the cylinder is \(\small v=10.5\).
Scheme of spatial solution
\(\small P \) midpoint of the line segment \(\small \overline {GH}\), \(\small P \in \Sigma\), \(\small \overline {GH} \perp \Sigma\) and the radius is \(\small \overline {SG}\). \(\small U \in o \), \(\small d(S,U)=v\). 
Solution via Monge's method (step by step)

Final drawing
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja