Question

A cylinder of maximum possible volume is carved out of a cube of edge $14\mathrm{cm}$. Find the volume of the cylinder (in ${\mathrm{cm}}^3$ ).

• A. 4312
• B. 2156
• C. 164
• D. 1617

Answer 1

Answer: (B)

The base diameter of the cylinder = the edge of the cube
$\therefore 2r=14\Rightarrow r=7\mathrm{cm}$
The height of the cylinder = the edge of the cube $=14\mathrm{cm}$
The curved surface area $=\pi r^{2}h$
$=\frac{22}{7}\times (7{)}^2\times 14=2156{\mathrm{cm}}^3$