The correct answer is option B: sphere.


A sphere is a three-dimensional shape that is perfectly round in shape, similar to a ball. It is a solid object that is formed by rotating a circle around its diameter.


When we talk about a shape rolling, it means that the shape can move by rotating along a surface without sliding or slipping. The rolling motion is similar to the way a ball rolls on the ground.


A sphere has the following characteristics that make it capable of rolling in any direction:

- Uniform Shape: A sphere has a uniform shape, meaning that all its points are equidistant from the center. This uniformity allows the sphere to roll smoothly without getting stuck or changing its direction.

- Smooth Surface: The surface of a sphere is smooth, without any edges or corners. This smooth surface reduces friction and allows the sphere to roll easily in any direction.

- Equal Distribution of Mass: The mass of a sphere is evenly distributed throughout its volume. This balanced mass distribution helps maintain stability while rolling and prevents the sphere from toppling over.

- Rotational Symmetry: A sphere has rotational symmetry around any axis passing through its center. This means that no matter which direction the sphere is rolled, it will always look the same.


Due to its uniform shape, smooth surface, balanced mass distribution, and rotational symmetry, a sphere can roll in any direction. When a force is applied to a sphere, it starts rolling and continues to roll without changing its direction until another force acts upon it.

In contrast, other shapes like a cube, rectangular prism, or polygon have flat surfaces and corners, which make them unable to roll in all directions. These shapes tend to slide or topple over when force is applied, limiting their ability to roll freely.

Therefore, a sphere is the only three-dimensional shape among the given options that can roll in any direction.