Write 'True' or 'False' and justify your answer:
If a solid cone of base radius $r$ and height $h$ is placed over a solid cylinder having the same base radius and height as that of the cone,then the curved surface area of the shape is $\pi r \sqrt{h^{2} + r^{2}} + 2 \pi r h$.

(A) True.
The curved surface area of the combined shape is the sum of the curved surface area of the cone and the curved surface area of the cylinder.
The curved surface area of a cone is given by $\pi r l$,where $l = \sqrt{h^{2} + r^{2}}$ is the slant height.
Thus,the curved surface area of the cone is $\pi r \sqrt{h^{2} + r^{2}}$.
The curved surface area of a cylinder is $2 \pi r h$.
Therefore,the total curved surface area of the combined shape is $\pi r \sqrt{h^{2} + r^{2}} + 2 \pi r h$.