The following operations are done on the curve shown in the figure. 1. The curve is revolved 360 degrees around the Y axis. 2. The resulting form is then cloned twice around the X axis at 120 degrees to each other. 3. The resulting form is then cloned once about the Y axis at 90 degrees. What is the resulting 3D form?
The problem involves several transformation operations on a given curve. Let's analyze each step and visualize the final 3D shape:
Revolution around the Y axis: Revolving the curve 360 degrees around the Y axis will generate a symmetrical 3D shape. This process typically results in a solid of revolution, such as a torus or a sphere, depending on the initial curve. Here, the revolution would create a cylindrical or toroidal shape around the Y axis.
Clone twice around the X axis at 120 degrees: After the revolution around the Y axis, we clone this shape twice, rotating each by 120 degrees relative to the previous one around the X axis. This will create a series of three intersecting shapes evenly distributed in a circular pattern around the X axis.
Clone once about the Y axis at 90 degrees: Finally, the entire form (composed of the three intersecting shapes) is cloned and rotated 90 degrees around the Y axis. This results in a symmetrical configuration of intersecting forms in both X and Y directions.
The set of operations results in a complex 3D symmetrical figure composed of several intersecting shapes. Referring to the given options and based on typical outcomes of rotational and cloning symmetry, the most probable resultant figure matches to:Thus, the correct resulting 3D form is represented by Fig 2.
