Chapter 11 - Geometry

circumference of a circle

2 x pie x radius or pie x diameter

arc length

arc length = measure in degrees/360 x 2 x pie x r (only arc length!)

ratio

arc LENGTH/2 x pie x r = measure in degrees/360 (finding anything else but the arc length!)

area of a circle

pie x radius^2

area of a sector

A = angle measure / 360 x pie x radius^2

OR

A (ratio) = area of a sector / pie x r^2 = angle measure /360

area of a rhombus

1/2 x diagonal x diagonal

center

equidistant to the vertices

apothem

distance from the center to a side (NOT THE RADIUS!)

central angle

formed by two consecutive radii, each angle measure of a regular n-gon is 360/n

area of a regular polygon

A = 1/2 x apothem x Perimeter

polyhedron

Formed by four or more polygons that intersect only at their edges. Prisms and pyramids are polyhedrons, but cylinders and cones are not.

face

Each flat surface

edge

segment that is the intersection of two faces.

vertex

the point that is the intersection of three or more faces.

cross section

The intersection of a three-dimensional figure and a plane.

solids of a revolution

3D figure that is formed by rotating a 2D shape around an axis

volume of a prism

v = Bh

volume of a cylinder

v = pie x r^2 x h

triangular prism base

B = 1/2 height x half of base

similar solids

two solids of the same type with equal ratios (scale factors) of corresponding linear measures, if two similar solids have a scale factor of k, then the ratio of their volume is equal to k^3

composite side

volume - other shape volume OR volume + other shape volume… depends!

volume of a pyramid

1/3 x B x h

surface area of a cone

pie x r^2 + pie x r x l (area of lateral surface)

volume of a cone

1/3 x pie x r^2 x h

great circle

divides a sphere into two hemispheres

surface area of a sphere

4 x pie x r^2

volume of a sphere

4/3 x pie x r^3

surface area of a hemisphere

3 x pie x r^2

volume of a hemisphere

2/3 x pie x r^3

area of a trapezoid

1/2 x (b+b) x h