Question

A cylinder of maximum volume is cut out from a wooden cuboid of length $30$ cm and cross-section a square of side $14$cm. Find the volume of the cylinder and the volume of wood wasted.

Answer 1

$\begin{array}{c}Cylinde{r}^{\prime }sVolume,\\ radius=7cm\\ H=30\\ Volume=\frac{22}{7}\times 7\times 7\times 30\\ =4620c{m}^3\\ Volumeofcuboid=14\times 14\times 30=5880\end{array}$

Remaining volume of wood

$5880-4620=1260c{m}^3$