$A$ line segment $l$ of length $a \ cm$ is rotated about a vertical line $L$ keeping the line $l$ in one of the following three positions: $(I)$ $l$ is parallel to $L$ and is at a distance of $r \ cm$ from $L$,$(II)$ $l$ is perpendicular to $L$ and its mid-point is at a distance $r \ cm$ from $L$,$(III)$ $l$ and $L$ are in the same plane and $l$ is inclined to $L$ at an angle $30^{\circ}$ with its mid-point at a distance $r \ cm$ from $L$. Let $A_1, A_2, A_3$ be the areas so generated. If $r > (a / 2)$,then

• A
  $A_1 < A_3 < A_2$
• B
  $A_2 < A_1 < A_3$
• C
  $A_1 = A_3 < A_2$
• D
  $A_1 = A_2 = A_3$