From a solid wooden cube with edge length 4.2 decimeters, determine the volume of the largest possible solid right circular cone that can be carved out with minimal wood wastage.

Q.From a solid wooden cube with edge length 4.2 decimeters, determine the volume of the largest possible solid right circular cone that can be carved out with minimal wood wastage.

The diameter and height of the right circular cone will be 4.2 decimeters. ∴ The volume of the cone is: \[ \frac{1}{3} \pi \left( \frac{4.2}{2} \right)^2 \times 4.2 \text{ cubic decimeters} \] \[ = \frac{1}{3} \times \frac{22}{7} \times \left( \frac{21}{10} \right)^2 \times \frac{42}{10} \text{ cubic decimeters} \] \[ = \frac{22 \times 21 \times 21 \times 42}{3 \times 7 \times 10 \times 10 \times 10} \text{ cubic decimeters} = 19.404 \text{ cubic decimeters} \] Therefore, the volume of the largest possible solid right circular cone is 19.404 cubic decimeters.