Let $O$ be the vertex (apex) of a right circular cone such that the radius of the base is 1 and the slant height is 3. (1) Consider the net of the cone, which consists of a sector and a circle. (The net of a solid is a 2-dimensional shape that can be folded to form that solid.) The central angle of the sector is $\square$ ABC , and the area of the sector is $\square$ D $\pi$. (2) Take two points A and B on the circumference of the base such that the line segment AB is a diameter. Take a point P on the segment OB and consider a path on the side of this circular cone which starts from the point A , passes through the point P and returns to A . Denote the length of the path by $\ell$. (i) If $\mathrm { OP } = 2$, then the smallest value of $\ell$ is $\mathbf { E }$. $\mathbf { F }$. (ii) Let point P be any point on the line segment OB . When $\ell$ is minimized, then $\mathrm { OP } = \frac { \mathbf { G } } { \mathbf { G } }$, and the value of $\ell$ is $\square \sqrt { } \square$.
Let $O$ be the vertex (apex) of a right circular cone such that the radius of the base is 1 and the slant height is 3.
(1) Consider the net of the cone, which consists of a sector and a circle. (The net of a solid is a 2-dimensional shape that can be folded to form that solid.) The central angle of the sector is $\square$ ABC , and the area of the sector is $\square$ D $\pi$.
(2) Take two points A and B on the circumference of the base such that the line segment AB is a diameter. Take a point P on the segment OB and consider a path on the side of this circular cone which starts from the point A , passes through the point P and returns to A . Denote the length of the path by $\ell$.
(i) If $\mathrm { OP } = 2$, then the smallest value of $\ell$ is $\mathbf { E }$. $\mathbf { F }$.
(ii) Let point P be any point on the line segment OB . When $\ell$ is minimized, then $\mathrm { OP } = \frac { \mathbf { G } } { \mathbf { G } }$, and the value of $\ell$ is $\square \sqrt { } \square$.