In the context of a cylinder, the statement "The bases of a cylinder must be polygons" is true. A cylinder is a three-dimensional shape that consists of two parallel, congruent circular bases connected by a curved surface. The bases of a cylinder are always circles, which are considered polygons.
Here's why the statement is true:
1. A polygon is a closed two-dimensional shape made up of straight lines. A circle can be considered a polygon with an infinite number of sides because it is made up of an infinite number of points equidistant from the center. Therefore, a circle qualifies as a polygon.
2. In the case of a cylinder, the circular bases can be seen as polygons with an infinite number of sides due to the continuous nature of the circle. Even though circles are not typically referred to as polygons in common terminology, they can be mathematically classified as such.
3. Since the bases of a cylinder are circular (considered as polygons with infinite sides), the statement holds true that the bases of a cylinder must be polygons.
So, in summary, the bases of a cylinder, though circular in shape, can be mathematically considered as polygons, supporting the statement that the bases of a cylinder must be polygons.
