A 'Square' (a 2D figure) is related to 'Cube' (its 3D counterpart) in the same way as a 'Circle' is related to which 3D counterpart?

Introduction / Context:
This analogy connects a two-dimensional shape to its three-dimensional solid. A square (2D) corresponds to a cube (3D) through the idea of extending the figure into space. We must apply the same 2D → 3D relationship to a circle.

Given Data / Assumptions:

• Square is a plane figure; cube is a solid.
• Circle is a plane figure.
• We need the 3D solid naturally associated with a circle.

Concept / Approach:
When a circle is extended uniformly in three dimensions (by revolution about a diameter), the resulting solid is a sphere. The mapping preserves the idea of 'shape to corresponding solid'.

Step-by-Step Solution:
1) Recognize relation: 2D plane figure → 3D solid.2) Square corresponds to cube; seek circle's 3D analog.3) Circle revolved about a diameter produces a sphere.4) Therefore, circle → sphere.

Verification / Alternative check:
Geometric solids of revolution: circle about its diameter gives sphere; about an axis coincident with its diameter also yields sphere, confirming the mapping.

Why Other Options Are Wrong:

• Circumference: A property/measurement of a circle, not a 3D solid.
• Diameter: A linear measure across a circle; not a 3D object.
• Area: A measure of extent in 2D; not a solid.
• None of these: Incorrect because 'Sphere' fits perfectly.

Common Pitfalls:
Choosing a property (circumference/diameter) rather than the correct 3D analog. Keep the dimension shift consistent.

Final Answer:
Sphere