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Q.
A cylinder of maximum possible volume is carved out of a cube of edge $14 \mathrm{~cm}$. Find the volume of the cylinder (in $\mathrm{cm}^3$ ).
Mensuration
Solution:
The base diameter of the cylinder = the edge of the cube
$\therefore 2 r=14 \Rightarrow r=7 \mathrm{~cm}$
The height of the cylinder = the edge of the cube $=14 \mathrm{~cm}$
The curved surface area $=\pi r^2 h$
$=\frac{22}{7} \times(7)^2 \times 14=2156 \mathrm{~cm}^3$