Which one of the following figures will generate a cone when rotated about one of its straight edges?

### Concept & Solid of Revolution A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line (the axis of revolution) that lies on the same plane. When a 2D shape is spun rapidly around a straight edge, it forms a 3D volume. ### Step-by-Step Solution - **Analysis of Options:** - **(a) An equilateral triangle:** Rotating this about an edge creates two cones stuck together at their bases (a bi-cone). - **(b) A sector of a circle:** Rotating this creates a spherical sector or a fraction of a sphere depending on the axis. - **(c) A segment of a circle:** Generates a complex shape or a portion of a sphere, not a simple cone. - **(d) A right-angled triangle:** Rotating a right-angled triangle about either its perpendicular or its base perfectly sweeps out a right circular cone. The rotated edge becomes the height, the other leg becomes the radius of the base, and the hypotenuse becomes the slant height. ### Exam Strategy & Shortcut Visualize the spinning motion. A cone requires a flat base (swept by a perpendicular leg) and a straight tapering side (the hypotenuse). Only a right-angled triangle has these exact properties when rotated about a leg. ### Common Pitfall Confusing an equilateral triangle with a right triangle; while an equilateral triangle *contains* right triangles, spinning it by its edge creates a double cone, not a single standard cone. ### Final Answer Therefore, the correct answer is **A right-angled triangle**.