Which of the following three-dimensional geometric shapes is always formed by a net that consists of only one type of shape?

Rationale

Cube is always formed by a net that consists of only one type of shape.

A cube consists entirely of six identical square faces, making it a three-dimensional solid that can be represented by a net comprising only squares. This uniformity in shape across all faces distinguishes the cube from other geometric shapes which may utilize different shapes in their nets.

A (Cylinder) YOUR ANSWER

A cylinder is composed of two circular bases and a curved rectangular surface connecting them. The net of a cylinder consists of both circles and rectangles, leading to a combination of different shapes rather than just one type. Therefore, it does not meet the criterion of being formed solely from one shape.

B (Cube) CORRECT

A cube's net consists entirely of six squares, which are uniform in shape. This essential characteristic allows the cube to be uniquely identified as a three-dimensional figure that can be unfolded into a flat net made up exclusively of one type of polygon, satisfying the question's requirement.

C (Prism) YOUR ANSWER

A prism can have various bases (triangular, rectangular, etc.) and consists of two identical bases and additional rectangular faces connecting them. The net of a prism will feature different shapes depending on the type of base used, thus failing to meet the condition of being formed by a net of only one type of shape.

D (Pyramid) YOUR ANSWER

A pyramid consists of a polygonal base and triangular faces that converge at a single point. The net of a pyramid includes both the base shape (which can vary) and several triangles, indicating that it is composed of more than one type of shape. Therefore, it does not satisfy the requirement of a net formed by a single shape.

Conclusion

Among the options, only the cube is characterized by a net that consists entirely of one type of shape—squares. This distinct feature sets the cube apart from cylinders, prisms, and pyramids, which each require multiple shapes in their respective nets. Understanding these properties is crucial in geometry, where the classification of shapes and their representations directly influences the study of spatial relationships and dimensional reasoning.

Which of the following three-dimensional geometric shapes is always formed by a net that consists of only one type of shape?

Cube is always formed by a net that consists of only one type of shape.

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