Find the volume of the largest right circular cone that can be fitted in a cube whose edge is $$14$$ cm $$($$in $$cm^3)$$.
Correct option is A. $$718.66 $$
Consider a right circular cone inserted in a cube.
Given, edge of cube $$=14 cm$$.
The maximum height can be equal to the edge of the cube.
Therefore, the height $$h=14 cm$$.
Also, the diameter of the cube will be equal to the edge of the cube.
Therefore, the height $$d=14 cm$$.
Then, radius $$r=\dfrac{d}{2}=\dfrac{14}{2}=7cm$$.
We know, the volume of a cube $$V=\dfrac{1}{3} \pi r^2 h$$
$$=\dfrac{1}{3} \times \dfrac{22}{7} \times (7)^2 \times (14)$$
$$=\dfrac{1}{3} \times 22 \times 7 \times 14$$
$$=718.66 cm^3$$.
Therefore, the volume of the largest circular cone is $$718.66 cm^3$$.