Final answer:
A square relates to a cube as a circle relates to a sphere because a square and circle are two-dimensional shapes, while a cube and a sphere are three-dimensional. The circle and sphere move from perimeter and area to circumference and surface area, eventually stepping up to volume in three dimensions.
Step-by-step explanation:
When comparing shapes in a dimensional context, a square is to a cube as a circle is to a sphere. This is because both a square and a circle are two-dimensional shapes, while a cube and a sphere are their three-dimensional counterparts. The square has a perimeter of 4a (where a is the side length) and an area of a². Similarly, a circle with a radius r will have a perimeter (circumference) that is smaller than the perimeter of the square but certainly more than its own diameter, leading to the perimeter formula of 2πr. A cube, stepping up a dimension, has a volume of a³ and a surface area of 6a², while a sphere, following suit, has a volume of 4/3πr³ and a surface area of 4πr². Here we see the progression from flat (two-dimensional) shapes to solid (three-dimensional) forms.