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V = Bh

Volume of ANY prism

Volume of Cylinders

V = Bh

Volume of Cones

V = 1/3Bh

V = 1/3Bh

Volume of *Rectangular* Pyramids

polyhedron

a 3D solid with many faces

polygon

a closed figure made by joining line segments where each line segment intersects exactly 2 others

rotation

It is a transformation that turns a figure about a fixed point.

cross-section

cut it, pick it up and look where you cut... what shape do you see?

Apothem

The perpendicular distance from the center to a side of a regular polygon.

surface area

the total area of each surface or face added together

volume

measures the amount of space taken up by the object.

net

a 2-dimentional pattern that can be folded to make a 3-dimentional solid

pentagon

a 5 sided polygon

hexagon

a 6-sided polygon

heptagon

a 7-sided polygon

octagon

an 8-sided polygon

nonagon

a 9-sided polygon

decagon

a 10-sided polygon

½b(h)

area of a triangle

b(h)

Volume of a Prism

½(d₁)(d₂)

area of rhomubs or kite

½(h)(b₁+b₂)

area of a trapezoid

Πr²

Area of circle

SA of a Prism

SA = 2lw + 2lh + 2wh

Ph

Prism LA

LA+2B

Prism SA

bh

Prism V

1/2PL

Pyramid LA

LA+B

Pyramid SA

1/3Bh

Pyramid V

2πrh

LA of Cylinder

LA+2πr²

Cylinder SA

πr²h

V of cylinder

πrL

LA of Cone

LA+πr²

Cone SA

1/3πr²h

Cone V

4πr²

SA of Sphere

4/3πr³

V of Sphere

prism

A solid geometric figure whose two end faces are similar, equal and parallel rectilinear figures, and whose sides are parallelograms.

cylinder

A solid shape with one curved surface and two congruent circular bases.

cone

A solid shape with a circular base and a curved surface that come to a point (vertex).

pyramid

A solid shape with a polygon as a base and triangular faces that come to a point (vertex or apex)

V=4/3(pi)r3

Sphere (Volume)

S=4(pi)r2

Sphere (Surface Area)

faces

the faces of a polyhedron (polygons) that enclose a single region of space

edge of a polyhedron

a line segment formed by the intersection of two faces in a polyhedron

vertex of a polyhedron

a point where three or more edges meet

bases of a prism

congruent polygons in parallel planes

Euler's Theorem

The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F+V=E+2.

regular polyhedron

is a polyhedron with faces bounded by congruent regulaar polygons and with the same number of faces intersecting at each vertex.

convex polyhedron

any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron

concave polyhedron

if any two points on its surface are connected by a segment that goes outside the polyhedron

Platonic solids

regular tetrahedron (4 faces), cube (6 faces), regular octahedron (8 faces), regular dodecahedron (12 faces), regular icosahedron (20 faces)

regular tetrahedron

4 faces

cube

A solid shape that has: 6 square faces all equal in size, 8 vertices (corners), and 12 equal edges.

regular octahedron

8 faces

regular dodecahedron

12 faces

regular icosahedron

20 faces

cross section

the intersection of a plane and a solid

lateral faces

parallelograms formed by connecting the corresponding vertices of the bases (faces that aren't the bases)

lateral edges

the segments connecting the lateral faces

lateral area

the sum of the areas of its lateral faces

surface area of a prism

S = 2B + Ph

height of a prism

the perpendicular distance between its bases

right prism

each lateral edge is perpendicular to both bases

oblique prism

prism with lateral edges that are not perpendicular to its bases

height of a cylinder

the perpendicular distance between its bases

radius of a base

radius of the cylinder

right cylinder

the segment joining the centers of the bases is perpendicular to the bases

surface area of a cylinder

SA = 2 pi r squared + 2 pi r h