final unit. i need to do well. Flashcards
3D spatial figure
solid
geometric solid with polygon as faces
polyhedron
one of the polygons that form the polyhedron
face of a polyhedron
intersection of two faces of a polyhedron
edge
intersection of two or more edges
vertex
the face that is formed when you make a slice through an object
cross sections
not all cross sections need to be parallel to a face & **the number of faces dictates the maximum number of sides a cross section can have**
rules of a cross section
cross sections can’t be circles because you can’t slice a curve, and the maximum number of sides is a 6 so you can’t have cross sections for octagons or decagons
what is the max number of sides of a polygon cross section for a triangular prism
5 (5 faces)
you can create a rectangle as a cross section for a cylinder because if you slice a cylinder perpendicular it should create a rectangle
what are the possible cross sections for a sphere
circles.
stacking principle of the volume of a prism
there’s literally 2 congruent translated bases already in a prism so the cross sections are identical to those bases
all of the cross sections are identical to the bases in a prism because we have 2 translated congruent bases in parallel planes, so to calculate the volume of a prism, calculate the area of the base and then multiply it by the height of the prism
Vprism= Bh
*B is the area of the base
Volume of a prism
If the AREA OF THE CROSS SECTIONS ON BOTH SOLIDS by any plane II to a given plane are invariably equal, the solids have the same volume
If a right prism and oblique prism have the same height and the same base, they have the same volume
Cavalieri Principle
revolving 2-d shapes creating a cylindrical shape- figures are rotated about an axis to fill space and create volume
a polyhedron with bases (in parallel planes) that are 2 congruent polygons
prism
the other side off the prism when bases of the prism are in parallel planes
lateral faces
the base and lateral edges are perpendicular to each other, and the height of the prism is a lateral edge
right prisms
the perpendicular distance between the two congruent bases
height of a prism
when the base and lateral edges are not perpendicular, the lateral faces are parallelograms instead of rectangles
oblique prism
perimeter x height
lateral area
lateral area + area of the bases (LA + 2B)
surface area
2pirh
lateral area for a cylinder
2pirh + 2(pir2)
surface area for a right cylinder
Bh aka (pir2) (h)
volume of a cylinder
1/2pl
LA of a pyramid
1/2pl+B
SA of a pyramid
1/3Bh
volume of a pyramid
pi(r)(l)
LA of a cone
pi(r)(l) + (pi)(r2)
SA of a cone
1/3(pi)(r2)(h)
volume of a cone
how to get volume of a truculated cone
1)proportions between both triangles
2)find volumes for both (1/3(pi)(r2)(h) ) and then subtract from each other
4(pi)(r2)
SA & LA of a sphere
4/3(pi)(r3)
volume of a sphere, this is halved for a hemisphere
composite figures
find areas/volumes for each basic figure and then add together
Formula for density
D= M/V
Formula for population density
population density= population/land area
area of a circle
pi r2
