82. Which of the following three-dimensional geometric shapes is always formed by a net that consists of only one type of shape?
Answer: B
A cube is always formed by a net that consists of only one type of shape.
A cube is composed entirely of square faces, making it unique among the listed options in that its net is formed by multiple squares.
A) Cylinder
A cylinder is formed by a net that includes both circular and rectangular shapes. This combination of different types of shapes disqualifies it from being the correct answer since it does not consist of only one type of shape.
B) Cube
A cube's net comprises only squares, which means it is always formed by a net that consists of only one type of shape. This characteristic sets the cube apart from the other geometric shapes listed.
C) Prism
While some prisms can have faces that are all the same shape, most commonly they consist of two parallel bases that are the same shape and rectangular or other types of faces connecting them. Therefore, a prism does not always meet the requirement of being formed by a net of only one type of shape.
D) Pyramid
A pyramid typically consists of a base that is one shape (such as a triangle or square) and triangular faces connecting the base to a single vertex. As a result, it is not formed by a net of only one type of shape, making it an incorrect option.
Conclusion
The cube is the only shape among the options that is formed by a net consisting exclusively of one type of shape—squares. The other options either involve multiple types of shapes or do not consistently use a single shape across their nets, reinforcing that the cube is the definitive answer in this context.