geom unit 4

Volume of a prism/cylinder

V = BH, where B is the area of the base and H is the height.

Lateral surface area

The area of all the sides of the object, excluding its base and top.

Total surface area

The lateral surface area together with the areas of the base and top.

Lateral Surface Area formula

L = PH, where P is the perimeter of the base and H is the height of the prism.

Surface Area of a Prism

SA = PH + 2B, where P is the perimeter of the base, H is the height, and B is the area of the base.

Altitude of a pyramid

A perpendicular line segment that joins the vertex to the plane of the base.

Base edge

One of the edges of a base of a prism or pyramid.

Height

The length of an altitude of a geometric figure.

Lateral edge

An edge of a polyhedron that is not a base edge.

Pyramid

A three-dimensional figure with one base that is a polygon, and all other faces are triangles that meet at a single vertex.

Regular pyramid

A pyramid with a base that is a regular polygon and lateral faces that are congruent isosceles triangles.

Slant height

The length of the altitude of a lateral face of a pyramid.

Vertex of a pyramid

The common vertex at which the triangular faces meet.

Volume of a pyramid

V = BH, where B is the area of the base and H is the height of the pyramid.

Cone

A solid figure with a circular base and a curved surface that forms a point at the top.

Oblique cone

A cone whose axis is not an altitude.

Volume of a circular cone

V = 1/3BH or V = 1/3πr²H, where B is the area of the base, H is the height, and r is the radius of the cone.

Surface Area of a Cone

SA = πrl + πr², where r is the radius of the base and l is the slant height.

Annulus

The region between two concentric circles.

Center of a sphere

The point to which all points on the surface of a sphere are equidistant.

Sphere

A figure in space made up of all points equidistant from a given point.

Volume of a Sphere

V = 4/3πr³, where r is the radius of the sphere.

Surface Area of a Sphere

SA = 4πr², where r is the radius of the sphere.

Side/Perimeter Ratio/Scale Factor

A ratio comparing the sides or perimeters of two similar figures.

Area/Surface Area Ratio

A ratio comparing the area of two figures squared.

Volume Ratio

A ratio comparing the volumes of two similar figures cubed.