Volume Mind Map
2-Dimension to 3-Dimension
Cross section of a pentagonal pyramid : Pentagon
Solid of revolution for a triangle : Cone
Cross section of a rectangular prism : Rectangle
Solid of revolution for a semicircle : Sphere
Prisms and Cylinders
Volume of a Cylinder : V=πr²h
Cavaleri's Principal : A skew figure of equal base and height will have the same volume as a right-angled figure
Volume of a Prism : V=Bh where B is the area of the base and h is the height.
Pyramids and Cones
Volume of a Pyramid : V = 1/3Bh
Volume of a Cone : V=1/3πr²h
Spheres
Volume of a Sphere : V = 4/3πr³
Hemisphere: half a sphere created by a great circle
Surface Area of a Sphere : SA = 4πr²
Spherical Geometry
Non-Euclidean Geometry : a type of spherical geometry
Great Circle : the intersection of a sphere and a plane containing the center of the sphere
Euclidean Geometry : A geometrical system in which a plane is a flat surface made up of points that extend infinitely in all directions.
Line on a Sphere : a great circles
Triangle on a Sphere : the shape formed by the intersection of three line segments on a sphere
Transformations
Scale Factor : the ratio of the lengths of two corresponding sides of two similar polygons
Similar Geometric Solids : two solids that have an equal cubed scale factor
Dilation : A transformation that changes the size of an object, but not the shape.
Congruent Geometric Solids : two solids that have equal volume
Measurements
population density : Number of individuals per unit area
Density : Mass per unit volume