most unsharpened pencils are hexagonal prisms. describe a vertical and horizontal cross section of a pencil

horizontal: hexagon

vertical: rectangle (pencil is unsharpened!)

A vertical cross-section of an unsharpened pencil would be a circle. When you cut the pencil vertically from top to bottom, you would see a round shape, resembling a circular or elliptical disc.

A horizontal cross-section of an unsharpened pencil would be a regular hexagon. If you were to cut the pencil horizontally across its width, you would observe a six-sided polygon with straight sides and equal angles. This cross-section is commonly known as a hexagonal prism.

Sure! To describe a vertical and horizontal cross section of a pencil, let's start with the vertical cross section.

Vertical cross section:
A vertical cross section of a pencil is taken along a plane that cuts through the pencil vertically, from the tip to the eraser. Most unsharpened pencils have a hexagonal shape, which means they have six sides. When you cut a pencil along a vertical plane, the resulting cross section will also have a hexagonal shape.

Horizontal cross section:
A horizontal cross section of a pencil is taken along a plane that is perpendicular to the length of the pencil, cutting across it horizontally. In the case of a hexagonal pencil, this cross section would be a regular hexagon viewed from the top. Each side of the hexagon would be parallel to the table surface.

To visualize these cross sections better, you can imagine looking at the end of a pencil directly from above to see the horizontal cross section. For the vertical cross section, picture cutting the pencil lengthwise and examining the shape from the side.

Additionally, keep in mind that although most pencils are hexagonal, there might be variations in shape, such as round or triangular pencils. However, the vertical and horizontal cross sections for these shapes will have different characteristics compared to the hexagonal ones I described.