Chapter on Formulas

A collection of flashcards based on formulas related to polyhedra, prisms, pyramids, cylinders, cones, spheres, and frustums.

Polyhedron

A solid whose faces are polygons.

Edge

The line where two faces of a polyhedron intersect.

Prism

A solid with two parallel and congruent bases connected by lateral edges.

Lateral edges

The edges that connect the corresponding vertices of the bases in a prism.

Lateral face

The faces of the prism that are not the bases.

Right prism

A prism whose lateral faces are rectangles.

Regular prism

A prism whose bases are regular polygons.

Lateral surface area

The sum of the areas of the lateral faces of a prism.

Total surface area

The sum of the lateral area and the area of the two bases in a prism.

Lateral area formula

LA = pH, where p is the perimeter of one base and H is the height of the prism.

Pyramid

A polyhedron with a polygon base and triangular lateral faces.

Regular pyramid

A pyramid with a regular polygon base and the apex directly above the base's center.

Surface area of a pyramid

SA = B + (1/2) * p * l, where B is the area of the base, p is the perimeter of the base, and l is the slant height.

Cylinder

A solid with two parallel circular bases.

Surface area of a cylinder

SA = 2πr² + 2πrh, where r is the radius and h is the height.

Lateral area of a cylinder

LA = 2πrh, where r is the radius and h is the height.

Cone

A solid with a circular base and a single vertex.

Lateral area of a cone

LA = πrl, where r is the radius and l is the slant height.

Surface area of a cone

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

Sphere

A perfectly round three-dimensional figure where every point on the surface is equidistant from the center.

Surface area of a sphere

SA = 4πr², where r is the radius.

Hemisphere

Half of a sphere, with surface area SA = 2πr².

Frustum

A cone with the top cut off, resulting in two circular bases.

Surface area of a frustum

SA = πR² + πr² + πl(R + r), where R is the radius of the larger base, r is the radius of the smaller base, and l is the slant height.