3D Equations

tried to calculate your surface area but my calculator maxed out...

polyhedron

a soild made up of polygons

face

polygons that form the soild

base

two congruent and parallel faces (prisms are called by their base shape)

lateral face

face that are not bases

altitiude (height)

perpendicular segment that joins the bases

right prism

lateral faces perpendicular base (lateral faces are rectangles, altitude is in the prism)

oblique prism

lateral faces are not perpendicular to bases (altitude is outside of prism, lateral faces are parallelograms)

lateral area: LA

P x h = Perimeter of the base x height of the prisim

Surface Area: SA

LA + 2B ( B=Area of the base)

Volume: V

Bh (Any polygon)

Cylinder Lateral Area

2pi * rh

Cylinder Surface Area

2pi x rh + pi x r²

Cylinder Volume

pi x r² x height

Sphere

set of all points in a space that are equidistant from a given point called the center

Great circle

widest path around a sphere. same radius as sphere that divides the sphere equally

Sphere Surface Area

4pi x r²

Sphere Volume

4/3 x pi x r³

ratio between areas in simliar figures

Side₁² : Side₂²

Side₁³ : Side₂²

vertex

point where all the triangles intersect

slant height

height of the triangular face (l)

Pyramid Lateral Area

½ x PL

Pyramid Surface Area

LA + B

Pryamid Volume

1/3 B H

Cone Lateral Area

pi x radius x slant height

Cone Surface Area

LA + B = pi x radius x slant height + pi x radius²