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pyramid

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

vertex of the pyramid

point where the triangles meet

regular pyramid

a pyramid that has a regular polygon for a base, the segment joining the vertex and the center of the base is perpendicular to the base

congruent isosceles triangles

lateral faces of a regular polygon

slant height of a regular pyramid

height of a lateral face of the regular pyramid

surface area of a pyramid

S = B + 1/2 PL

cone

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

radius of the base

radius of the cone

height of a cone

the perpendicular distance between the vertex and the base

right cone

segment joining the vertex and the center of the base is perpendicular to the base and the slant height is the distance between the vertex and a point on the base edge

slant height of a cone

the distance between the vertex and a point on the base edge

lateral surface of a cone

consists of all segments that connect the vertex with points on the base edge

surface area of a right cone

The surface area S of a right cone is S=B=1/2Cl=╥r^2=╥rl, where B is the area of the base, C is the circumference of the base, r is the radius of the base, and l is the slant height.

volume of a solid

the number of cubic units contained in its interior

volume fo a cube postulate

the volume of a cube is the cube of the length of its sides

volume congruence postulate

if 2 polyhedra are congruent, then they have the same volume

volume addition postulate

the volume of a solid is the sum of the volumes of all its non-overlapping parts

Cavalieri's Principle Theorem

if two solids have the same height and the same cross-sectional area at every level, then they have the same volume

V = Bh

Volume of ANY prism

Volume of a Pyramid

V = 1/3 lwh

Volume of a Cone

V = 1/3 pi r squared h

sphere

A solid shape that is perfectly round like a ball. No faces, edges, or vertices.

center of a sphere

point equidistant from all points of a sphere

S = 4πr²

surface area of a sphere

Great Circle

when a plane intersects a sphere and the plane contains the center of the sphere

Hemispheres

the separate congruent halves divided by the great circle

volume of a sphere

V = 2/3 pi r squared h (or) V = 4/3 pi r cubed

similar solids

two solids of the same type with equal ratios of corresponding linear measures (like height or radii)

similar solids theorem

If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a ²:b ², and corresponding volumes have a ratio of a³:b³.

Prism LA

Pb x h

Prism TA

LA + 2Ab

Prism Volume

Ab x h

Pyramind LA

½ Pb x Hs

Pyramind TA

LA + Ab

Pyramind Volume

⅓ Ab x h

Cylinder LA

Cb x h

Cylinder TA

LA + 2Ab

Cylinder Volume

Ab x h

Cone LA

πr x Hs

Cone TA

LA + Ab

Cone Volume

⅓ Ab x h

4πr²

SA of Sphere

⁴⁄₃πr³

Sphere Volume

V=s³

volume of a cube

V=Bh

Prism: Volume

V=πr²h

Volume of a Circular Cylinder

Cavalieri's Principal Theorem

If two solids have the same height and the same cross-section area at every level, then they have the same volume

V= 1/3Bh

Volume of a pyramid

V=1/3πr²h

Volume of Cone

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.

cross section

the intersection of a plane and a solid

V=4/3 πr³

Volume of a Sphere

V=2/3πr³

Volume of a hemisphere

Volume- Pyramid

V=1/3 Bh

SA=2B+Ph

Surface Area- Prism

Volume- Cone

V= 1/3 Bh

V=πr^2h

Volume of a Cylinder

SA=2πr^2+2πrh

Surface Area- Cylinder

V=4/3πr^3

Volume of a Sphere

SA=4πr^2

Surface Area of a Sphere

A=1/2 aP

Area of a Hexagon

Circumference

2πr

Cavalieri's Principle

Same Base - Same Height - Volumes are the Same.

Variable B

Base area

Variable P

Perimeter of the base

Variable h

Height of the prism

Variable l

Slant height

Definition of apothem

A line from the center of a regular polygon at right angles to any of its sides.

a^2 + b^2 = c^2

used to check side lengths in a right triangle