Unit 1
Glossary
Integrated Math 3
An apex is the single point on a cone or pyramid that is farthest from the base. For a pyramid, the apex is where all the triangular faces meet.
An axis of rotation is a line that a two-dimensional figure is rotated around to produce a three-dimensional figure, called a solid of rotation.
In this diagram, the dashed line is the axis of rotation for the solid of rotation formed by rotating the green triangle.
Cavalieri’s Principle states that if two solids of equal height are cut into cross-sections by parallel planes, and the corresponding cross-sections on each plane always have equal areas, then the two solids have the same volume.
A cone is a three-dimensional figure with a circular base and a point not in the plane of the base called the apex. Each point on the base is connected to the apex by a line segment.
From an earlier course.
A cross-section is the two-dimensional figure formed by intersecting a solid with a plane.
These diagrams show that the shape of the cross-section depends on how the plane intersects the solid.
The cube root of a number \(x\), written \(\sqrt[3]{x}\), is the number \(y\) whose cube is \(x\).
That is, \(y^3 = x\). So, \(\sqrt[3]{x}=y\).
Example: \(2^3 = 8\). So, \(\sqrt[3]{8}=2\).
A cylinder is a three-dimensional figure with two parallel, congruent, circular bases, formed by translating one base to the other. Each pair of corresponding points on the bases is connected by a line segment.
From an earlier course.
Density is a measure of how tightly the amount of matter in a substance is packed into the space it takes up. That is, density is the mass of a substance per unit volume.
\(\text{density}=\frac{\text{mass}}{\text{volume}}\)
Any flat surface on a three-dimensional figure is a face.
- A cube has 6 faces that are all squares.
- A cylinder has 2 faces that are both circles.
From an earlier course.
An oblique solid is not exactly upright—it seems to lean over at an angle.
- Prisms and cylinders are said to be oblique if the directed line segment that defines the translation between the bases is not perpendicular to the bases.
- A cone is said to be oblique if a line drawn from its apex at a right angle to the plane of its base does not intersect the center of the base. The same definition applies to pyramids whose bases are figures with a center point, such as a square or a regular pentagon.
A prism is a three-dimensional figure composed of two parallel, congruent faces (called bases) connected by parallelograms. A prism is named for the shape of its bases. For example, if a prism’s bases are pentagons, it is called a pentagonal prism.
rectangular prism
triangular prism
pentagonal prism
From an earlier course.
A pyramid is a three-dimensional figure that has one special face called the base. All of the other faces are triangles that meet at a single vertex called the apex. A pyramid is named for the shape of its base. For example, if a pyramid’s base is a hexagon, it is called a hexagonal pyramid.
square pyramid
pentagonal pyramid
From an earlier course.
A right solid is exactly upright—it does not seem to lean over at an angle.
- Prisms or cylinders are said to be right if the directed line segment that defines the translation between the bases is perpendicular to the bases.
- A cone is said to be right if a line drawn from its apex at a right angle to the plane of its base passes through the center of the base. The same definition applies to pyramids whose bases are figures with a center point, such as a square or a regular pentagon.
A solid of rotation is a three-dimensional figure formed by rotating a two-dimensional figure around a line called the axis of rotation.
In this diagram, the axis of rotation is the dashed line. The green triangle is rotated around the axis of rotation to form a solid of rotation.
A sphere is the set of all points in a three-dimensional space that are the same distance from a center point. All the cross-sections of a sphere are circles.
From an earlier course.