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

Largest size of cylinder cut out of the wooden cuboid will be of diameter = 14 cm, radius = $\dfrac{14}{2}$ = 7 cm and height = 30 cm.

Volume of cylinder = πr²h = $\dfrac{22}{7} \times 7 \times 7 \times 30$ = 22 × 7 × 30 = 4620 cm³.

Volume of cuboid = lbh = 30 × 14 × 14 = 5880 cm³.

Volume of wooden wasted = Volume of cuboid - Volume of cylinder = 5880 - 4620 = 1260 cm³.

Hence, the volume of cylinder = 4620 cm³ and volume of wooden wasted = 1260 cm³.