Question 60
A lamp, which is supposed to be point-like, is placed at a point $V$. It projects onto a plane $a$ located 2 meters from $V$ a beam of light having the shape of a circular cone with an axis perpendicular to $a$, whose generators form an angle of $30^{\circ}$ with the axis of the cone. On the $a$ plane, in the center of the base of the cone, a cardboard cube is placed, with an edge of 1 meter. We ask what the total area illuminated by the lamp is (on the $a$ plane and on the upper face of the cube), expressed in $\mathrm{m}^{2}$.