How is the radius for the pattern of a right cone obtained?

The radius for the pattern of a right cone is determined by the slant height of the cone, which is relevant when laying out the cone's development pattern. The pattern of a right cone consists of a sector of a circle, where the radius of this circle corresponds to the slant height of the cone. This is essential for getting the correct proportions when creating the flat pattern that will be rolled into the conical shape.

Understanding the geometry of the cone helps clarify why the slant height is the key measurement. The slant height is the distance from the apex of the cone to any point on the perimeter of the base. When unfolding the cone into a flat pattern, this slant height becomes the radius of the sector formed, allowing for correct proportions and ensuring the cone fits as intended when assembled.

The other choices relate to different aspects of the cone's geometry. For instance, using the base radius or diameter multiplied by Pi would not yield the correct measurement needed for developing the cone's pattern. The vertical height, while important for determining the cone's volume and shape, does not correspond directly to the design of the flat pattern either. Therefore, the focus on the slant length highlights its critical role in accurately constructing the cone's layout.