Consider the following figure: What solid 3D object is produced by rotating the semicircle about line m?
Answered on
Answer: When you rotate a semicircle about a line that corresponds to its diameter, the solid 3D object that is formed is a sphere.
Here's the logical step-by-step:
1. Visualize the semicircle with line m as the diameter. 2. As you rotate the semicircle about line m, every point on the curved edge of the semicircle traces out a circular path in three dimensions. 3. Since the semicircle is being rotated 360 degrees around its diameter, each of these paths will combine to fill out the entire surface of a sphere. 4. The resulting object has perfect symmetry about the axis of rotation (line m), meaning all points on the surface of the sphere are equidistant from the center of the sphere. 5. When the rotation is complete, you are left with a full sphere where the original line m becomes the diameter of this sphere.