1. Because of the picture. The line is tangent to the curve, indicating that both are the same width at the tangent point. If they were not the same size, the line would continue past the curve (larger width), or the base of the cone would overlap the line (larger cone base).
2. There is no dimension that says the cone is a different size at the base.
3. If you have the original picture, there should be a Section A-A view that will also show the base of the cone is at the length of the top leg. A top view would be clearer, if it exists.