Geometry: Euler's Formula and Surface Area

These flashcards cover key concepts related to Euler's Formula and the properties of various geometric solids including prisms, pyramids, and cylinders.

Euler's Formula

V - E + F = 2, which relates the number of vertices (V), edges (E), and faces (F) of a polyhedron.

Net

A 2-D representation of a 3-D figure that can be folded to form the 3-D object.

Cross-section

The intersection of a solid and a plane.

Prism

A solid shape that has two parallel bases connected by lateral faces.

Pyramid

A solid shape with a polygonal base and triangular faces that converge at a point (the apex).

Cylinder

A solid shape with two circular bases connected by a curved surface.

Parts of a prism

Base, lateral face, edges, altitude, and axis.

Lateral Area (LA) of a Cylinder

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

Surface Area (SA) of a Cylinder

SA = 2πrh + 2πr².

Lateral Area (LA) of a Pyramid

LA = (P-h), where P is the perimeter of the base and h is the slant height.

Surface Area (SA) of a Pyramid

SA = PL + B, where P is the perimeter of the base and L is the slant height.

Slant height

The height of a face of a pyramid or cone measured along the slant.