Solid Mensuration Practice Flashcards

Vocabulary practice flashcards covering terminology, definitions, and core formulas of solid geometry and mensuration.

Plane

A surface such that a straight line joining any two points in it lies wholly in the surface.

Parallel Planes

Two planes which do not intersect however far produced.

Dihedral Angle

The figure formed by two planes which cut each other.

Polyhedral Angle

The figure formed at a common point when three or more planes meet.

Perpendicular Planes

Two planes that form a dihedral angle whose plane angle is a right angle.

Section

The intersection of a solid and a plane.

Right Section

A section of a solid made by a plane perpendicular to the axis of the solid; often called a cross section.

Polyhedron

A solid bounded by polygons.

Convex Polyhedron

A polyhedron every section of which is a convex polygon.

Regular Polyhedron

A polyhedron all of whose faces are equal regular polygons, and all of whose polyhedral angles are equal.

The Five Regular Polyhedrons

Tetrahedron (4 faces), Hexahedron or Cube (6 faces), Octahedron (8 faces), Dodecahedron (12 faces), and Icosahedron (20 faces).

Prism

A polyhedron of which two faces are equal polygons in parallel planes (bases), and the other faces (lateral faces) are parallelograms.

Parallelopiped

A prism whose bases are parallelograms.

Right Prism

A prism whose lateral edges are perpendicular to its bases.

Rectangular Parallelopiped

A parallelopiped whose six faces are all rectangles.

Cube

A parallelopiped whose six faces are all squares.

Pyramid

A polyhedron of which one face, called the base, is a polygon of any number of sides and the other faces are triangles which have a common vertex.

Regular Pyramid

A pyramid whose base is a regular polygon whose center coincides with the foot of the perpendicular dropped from the vertex to the base.

Slant Height of a Regular Pyramid

The altitude of a lateral face of the regular pyramid.

Frustum of a Regular Pyramid

The portion of a regular pyramid included between the base and a section parallel to the base.

Prismatoid

A polyhedron all of whose vertices lie in two parallel planes.

Prismoidal Formula

$V = \frac{h}{6}(b + B + 4M)$ where $h$ is altitude, $b$ is upper base, $B$ is lower base, and $M$ is the mid-section area.

Cylindrical Surface

A surface generated by a moving straight line (generator) which is always parallel to its first position and always intersects a fixed plane curve (directrix).

Cylinder

A solid bounded by a closed cylindrical surface and two parallel planes.

Circular Cylinder

A cylinder which has a circular right section.

Right Circular Cylinder

A cylinder whose elements are perpendicular to its base and whose bases are circles.

Conical Surface

A surface generated by a moving straight line (generator) which always intersects a fixed plane curve (directrix) and always passes through a fixed point (vertex).

Cone

A solid bounded by a conical surface whose directrix is a closed curve, and a plane (base) which cuts all the elements.

Right Circular Cone

A cone whose base is a circle and whose axis is perpendicular to its base.

Frustum of a Right Circular Cone

The portion of a right circular cone included between the base and a section parallel to the base.

Theorems of Pappus and Guldin (Surface)

The area of a surface generated by revolving a plane curve about an external axis is $S = y \alpha L$, where $L$ is line length and $y \alpha$ is the distance its center of gravity moves.

Theorems of Pappus and Guldin (Volume)

The volume generated by revolving a plane area about an external axis is $V = y \alpha A$, where $A$ is generating area and $y \alpha$ is the distance its center of gravity moves.

Sphere

A solid bounded by a closed surface, every point of which is equidistant from a fixed point called the center.

Great Circle

A section of a sphere made by a plane passing through the center of the sphere.

Meridians

Great circles passing through the poles of the earth, perpendicular to the equator.

Zone

The portion of the surface of a sphere included between two parallel planes.

Spherical Segment

A solid bounded by a zone and the planes of the zone's bases.

Spherical Sector

A solid generated by rotating a sector of a circle about an axis which passes through the center but contains no point inside the sector.

Similar Polyhedrons

Polyhedrons that have the same number of faces, respectively similar and similarly placed, with corresponding polyhedral angles being equal.

Cavalieri’s Theorem

If in two solids of equal altitude the sections made by planes parallel to and at the same distance from their bases are always equal, the volumes of the solids are equal.