Question

The shaded plane given below is rotated clockwise around the given axis, up to an angle of 270 degrees. Draw the solid form resulting from this rotation.

Hint:

When visualizing a 3D solid from a 2D rotational motion, consider the bounding volume and symmetry of rotation to ensure accurate representation.

Answer 1

Step 1: Understanding solids of revolution.
- When a two-dimensional shape rotates around an axis, it generates a three-dimensional solid of revolution.
- In this case, the given shape rotates through 270 degrees, resulting in a partially formed solid.

Step 2: Constructing the final solid.
- The solid’s outer contour is determined by tracking the movement of the shape during rotation.
- Key features such as curvature, edges, and symmetry must be identified.
- The final shape will resemble a sculpted 3D form, influenced by the original cross-section.

Step 3: Representing the solid on an isometric grid.
- Utilize the isometric grid to maintain correct proportions.
- Draw reference curves to guide smooth rotational transitions.
- Apply shading techniques to enhance depth and three-dimensional perception.