Philfour Geometry : 3D Geometrical Objects - Introduction, Polyhedra, Surface Area, Volume & Skew Li

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Sincerely,

Dr. Christian Seberino

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Closed Caption:

I'm going to talk
about three-dimensional geometric
objects including polyhedra
surface area volume and
skew lines let me now
be fine work polyhedra are up
polyhedra are three-dimensional
geometric objects composed
I'll polygons okay
remember that polygons
are two-dimensional up
geometric objects up
composed strength line said
examples are polygons
include triangles squares pentagon's
hexagons and octagon ce let me now
draw two examples are
polyhedron
so
the egyption pyramids
correspond to
polyhedra
they correspond to he
pipe are polyhedron referred to as
a pyramid like when I drawn
their notice that pyramids
are composed one square
and for triangles okay
here's another example
a polyhedron that dice
in a typical board game
the dice correspond to polyhedron
specifically they correspond to
a type on polyhedron
refer to as me keep like when I'm
just wrong notice that
the cue is composed
are 6 squares okay
squares and triangles are both polygons
now
you may know that polygons
are regular if all
are their corresponding line segments
are congruent and all their
corresponding
angles are also cover likewise
polyhedra are referred to you
has being regular here
all the course sponding edges
or line segments are congruent and all
the
all goes are congruent that will imply
that all the polygons are
regular in a regular polyhedron
okay now I'd like to
briefly pop about volume
so
you may know that the way that
we determined the area a two-dimensional
geometric
here is we find the kuhen number
standard scientists where's
that he got to see him out space
alright likewise one-way
to measure
volume is to determine
the the the number a standard-sized
Hughes
that take up the same amount of space
alright so you can
talk about 8 three-dimensional geometric
object for example having a volume
20 cubic meters or
40 cubic feet right that means
40 cubic feet means that the space
take a nap is equivalent to the space
are
taken up by four cue such that
their on site looks sidelines
are all one for right
what about surface area so every three
dimensional geometric
object has a service okay
the area that surface is referred to as
the service
area so the surface
area I love a polyhedron
would be the sum the areas evolving
course
bonding polygons okay
now
let me part
abouts you lines so
in two dimensions every
here lines either
were parallel worry intersected
can you think of any other possibility
for two lines
I on a plane okay there are parallel
already they cross at one point now
in three dimensions there is a third
possibility
you can have lines that are neither
parallel
on nor are they intersect
okay law long arms
in lines that are neither parallel
nor intersecting are referred to as skew
lines
okay let me
dry picture and I will
sure you an example skew
alright I drawn EQ now
the bottom up the cue
if you can imagine it resting on a table
the square that's making contact with
the table has vertices abc&d
and that harp the opposite
side the site that's far
the face thats farthest from cable is
corresponds to the square with vertices
E
G&H now notice
that the line that overlaps with
line segment AB and the line that
overlaps with
lines segment see GE
notice that those two lines
are neither parent nor are the
intersecting okay
soaking seen it there's that
those two lines don't fall in either
those
I'm cases so those are examples
a skew lines alright can you see
other Pierzynski lines one about
the the line that overlaps
lines segment CE the
and be yeah
the line that overlaps lines and
be a okay and you could find other
examples
okay one more
how bout the line that overlaps
line same GH and
the line that overlaps lines segment BC
okay so I hope you get the idea
now let me show you
a calculation volume
answer series
so give me are few more seconds to
finish a picture
okay so I drawn a
picture that were that corresponds to a
box
cable box is a polyhedron with
signs with faces that
are rectangles and so I want to
calculate
the the follow you
and by the way are let's assume that
my Lancs are given in units meters
okay
so the sides have links to meters three
meters
in eighteen years now
we know
that the bomb
rectangle one with sides have linked to
readers any
years we know that that has in area
6 who wins square meters
okay so if I was packing cubes into this
box
then I can't make on I can make one
layer accuse
on that would cover the bottom and that
layer would have
a we would have 16 cutesy
now I could I can
I could fit three layers on top of each
other
okay the reason I can only fit three
layers because
the other dimension up
is three more years okay so therefore
the volume
the number love cubes with sides
length one meter that I can the in this
box
is 16 times
3 or eight times two times three okay
and that keen's 40 so
48 cubic meters
right now
what about the surface area
so to calculate the surface
area we add up
the Arians evolve the
rectangles okay
so the bottom rectangle Hansen
area 6 through and the
opposite rectangle hasn't area 6
who the on
the rectangle with respect to sides
would like two and three in serious
6 the opposite wrecking also has an area
6 and there's a vertical rectangle with
sides are link3 8 so that has an area
24 and the opposite rectangle has an
area
20 were so now we we can add up
I love those areas and get what's
referred to as the surfaces so let's go
ahead and do that
so nazis the first to give
30 to class 12-plus
40 8 so nice sixty
plus 32 is the equivalent summer
and so the answer is
mein bhi to
square meters not cubic meters because
we're talking about
and area okay
now
I would like you to do
example
would you we is calculate the volume and
surface area
the following polyhedron gimme a minute
to me
cocaine so I have another box
this one has signs a blank one feet to
feet
intensity so go ahead possibly doin fine
that volume insert the Syrian please
okay so I'll go ahead and do it as well
so
the on
were bono the
this face thats on the floor
you can imagine resting on the floor
that corresponds to a rectangle sides
that link one for
to for Sony area is to square feet
so that means I can it two kilos
with us hides a length 14 1i chemical 12
one make one layer cubes with at the
bottom
and then I could make ten layers if I
stacked vertical
so the volume there for
is to times him or
twinkie cubic
okay and now let's calculate the surface
area so I've got 6
rectangles whose I
area and the final so the bottom and top
pair
areas 18 square feet
two plus two and then
to vertical rectangles sounds like 20
and
to others
us faces vertical faces have signs that
link
pan so no
adding those numbers together we can get
the surface area it's either before plus
for me plus 20 so that gives
sixty Foursquare because again we're not
talking about
phone