The collisional cross section is an “effective area” that quantifies the likelihood of a scattering event when an incident species strikes a target species. The collisional cross sections typically denoted σ and measured in units of area.

The area of that cross section is the well known A = pi*R² which is colloquially pronounced as “pie are squared.” We will put aside the old joke that “Pie are not squared; pie are round” but we have to admit to ourselves that expressing area and having to work with the irrational number “pi” can get numerically awkward …

The cross-sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional object – such as a cylinder – is sliced perpendicular to some specified axis at a point. For example, the cross-section of a cylinder – when sliced parallel to its base – is a circle.

1a : a cutting or piece of something cut off at right angles to an axis also : a representation of such a cutting. b : section sense 3b. 2 : a measure of the probability of an encounter between particles such as will result in a specified effect (such as scattering or capture)

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Cross-section Examples The vertical cross-section of a cylinder is a rectangle, and the horizontal cross-section is a circle.

A prism is a 3D solid with a uniform cross-section. The two end faces of a prism are identical in shape and size. If you make a cut parallel to the ends, the cross-section exposed will be the same shape and size as the ends.

uniform cross-section. • a cross-section of a solid that is the. same size and shape as its base.

The formula at the top of the page can be used to find the volume of a cylinder because a cylinder has a constant cross-sectional area if it is sliced parallel to the circular face – the cross-sectional area is the area of the circle that forms the base of the cylinder, that is × (radius)2.

Prisms and cylinders have uniform cross-sections, but pyramids and cones do not.

a. A square cross section can be created by slicing the cube by a plane parallel to one of its sides. b. An equilateral triangle cross section can be obtained by cutting the cube by a plane defined by the midpoints of the three edges emanating from any one vertex.

A rectangular pyramid is sliced by a plane parallel to its base. Describe the cross section. The cross section will always be a rectangle. The closer the plane is to the base, the bigger the rectangle.

If you are asking about the shape of the cross section for a right circular cylinder, that is the case. A parabola or triangle can’t be sliced so the cross section is parallel or perpendicular to the base. If the cross section is parallel to the base, it is a circle.

Answer: The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising, because I have not seen geometric figures like those before.

Area=52 square units.

Rectangular Pyramid. A rectangular pyramid is a three-dimensional object with a rectangle for a base and a triangular face coresponding to each side of the base. The triangular faces which are not the rectangular base are called lateral faces and meet at a point called the vertex or apex.

The cross section is a rectangle. Figure 5 shows the cross section of a right rectangular pyramid through its apex and perpendicular to its base. The cross section is a triangle.

Horizontal cross sections are the same shape: they are all squares if the pyramid is square or rectangles if the pyramid is a rectangle pyramid. Vertical cross sections are different size: the closer we get to the edges, the smaller they become.

The slant height of an object (such as a frustum, or pyramid) is the distance measured along a lateral face from the base to the apex along the “center” of the face. In other words, it is the altitude of the triangle comprising a lateral face (Kern and Bland 1948, p. 50).