A cylinder is cut lengthwise and flattened, thereby forming a rectangle of dimensions $66 \mathrm{cm}\times 28 \mathrm{cm}$. Find the curved surface area and volume of the original cylinder.

 The radii of the bases of two solid metallic cones of same height $\mathrm{h}$ are ${\mathrm{x}}_{1 }\& {\mathrm{x}}_2$. If the two cones are melted together and recast into a cylinder of height $\mathrm{h}$, then show that the radius of the base of the cylinder is $\sqrt{\frac{1}{3}\left({{\mathrm{x}}^2}_{1 }+{{ \mathrm{x}}^2}_2\right)}$.

    A solid metallic cylinder and another solid metallic cone have the same height $\mathrm{h}$ and the same radius $\mathrm{r}$. If the two solids are melted together and recast into a cylinder of radius $\frac{1}{2}\mathrm{r}$, prove that the height of the new cylinder is $\frac{16}{3} \mathrm{h}$.