Solid Geometry Grade 11
Summary
TLDRThis instructional video script guides Grade 11 students through solid geometry exercises, focusing on orthographic projection to draw the front, top, and right views of a pyramid. The instructor emphasizes the importance of accurate measurements, using a compass, and understanding hidden details. They demonstrate the process step-by-step, including how to handle auxiliary views and cuts, and encourage students to practice for exams, noting the availability of matric past papers for additional practice.
Takeaways
- π The lesson is focused on solid geometry, specifically drawing orthographic projections of a pyramid with a 60Β° angle.
- π The pyramid has a base length of 75 units and side lengths of 30 units, with an auxiliary view provided for additional measurements.
- π The instructor emphasizes the importance of accurate measurements and the use of a compass for consistency.
- π The drawing process involves labeling the auxiliary view and using it to help visualize the shape for the top view.
- ποΈ The 'little man' perspective is used to determine which parts of the pyramid will be visible from the top view, including the use of dashed lines for hidden details.
- π The instructor explains the concept of 'cutting' the pyramid and how to represent this in the top view with solid lines and hatching.
- π The right view drawing process is similar, using the 45Β° line to transfer points from the front view to the side view.
- π The instructor advises on the importance of keeping rulers clean to avoid smudging and ensure neat work, especially during exams.
- π The right view includes identifying visible and hidden details, with the base of the pyramid partially visible and the top cut off.
- π¨ The instructor uses a highlighter to emphasize the cut lines and distinguish between solid and hatched areas in the drawing.
- π The script mentions that grade 11 students should use matric (final year) past papers for practice if grade-specific papers are unavailable.
Q & A
What is the main topic of the video script?
-The main topic of the video script is solid geometry, specifically drawing the front view, top view, and right view of a geometric shape in orthographic projection.
What is the angle of the pyramid mentioned in the script?
-The pyramid mentioned in the script is at an angle of 60Β°.
What are the measurements given for the prism in the script?
-The prism has a length of 75 and a side length of 30.
What is the purpose of the auxiliary view in the script?
-The auxiliary view is used to help in drawing the top and right views of the geometric shape by providing additional lines and points for reference.
What does the script suggest about the importance of keeping rulers clean?
-The script suggests that keeping rulers clean is important to ensure that the work looks neater, especially during exam or test season.
How does the script describe the process of drawing the top view?
-The script describes the process of drawing the top view by starting with the bottom line, measuring and transferring points from the front view to the top view, and using the auxiliary view for reference.
What is the significance of the 45Β° line in the script?
-The 45Β° line is significant in the script as it is used to transfer points from the front view to the top and right views, ensuring the correct angles for the geometric shape.
What does the script imply about the visibility of certain parts of the pyramid in the top view?
-The script implies that in the top view, the bottom of the pyramid is not visible, and parts of the pyramid at the back are represented by dashed lines, indicating hidden detail.
How should the hatching in the top view be done according to the script?
-The hatching in the top view should be done at 45Β° using a ruler and at equal intervals, with the hatching being lighter than the solid drawing.
What is the orientation of the 'little man' in the script when drawing the right view?
-The 'little man' in the script is standing to the side of the geometric shape, looking at it from the side, which influences what parts of the shape are visible in the right view.
What does the script suggest about the importance of the auxiliary view during exams?
-The script suggests that the auxiliary view is important during exams because marks can be deducted if it is not properly drawn or if it obstructs the visibility of the main views.
Outlines
π Introduction to Solid Geometry Drawing
The instructor begins by introducing a solid geometry drawing lesson for grade 11 students, focusing on orthographic projection. The lesson involves drawing the front, top, and right views of a geometric shape, specifically a pyramid at a 60Β° angle. Key measurements such as length, side length, and auxiliary view dimensions are discussed. The instructor emphasizes the importance of drawing in the correct orientation and provides a step-by-step guide on how to begin the drawing process, including the use of an auxiliary view for accuracy.
π Detailed Steps for Top View Drawing
This paragraph delves into the specifics of drawing the top view of the pyramid. The instructor guides students through the process of transferring points from the front view to the top view, using a 45Β° line and a grid system for accuracy. The concept of hidden details and how to represent them with dashed lines is introduced. The instructor also explains the importance of a clean ruler for neatness, especially during exams, and provides tips on how to avoid smudging and maintain clarity in the drawing.
ποΈ Drawing the Right View and Handling Cuts
The third paragraph continues the lesson with the drawing of the right view, explaining the perspective as if the viewer is standing to the side of the pyramid. The instructor outlines the process of transferring lines and points to create the right view, using the 45Β° line as a reference. The concept of cuts in the pyramid is introduced, with the instructor showing how to represent these cuts in the drawing and differentiate between visible and hidden parts. The importance of hatching at 45Β° and maintaining a consistent interval is highlighted.
π Conclusion and Note on Past Papers
In the concluding paragraph, the instructor wraps up the solid geometry drawing lesson and offers additional support to students, indicating a willingness to create more content if needed. The instructor also addresses the scarcity of grade 11 past papers and suggests using matric (final year) papers as an alternative. There is a commitment to inform students if relevant grade 11 papers are available and to ensure that the content provided is suitable for their level of study.
Mindmap
Keywords
π‘Solid Geometry
π‘Orthographic Projection
π‘Front View
π‘Top View
π‘Right View
π‘Auxiliary View
π‘Hidden Detail
π‘Sectioning
π‘Hatching
π‘Cut
π‘Measurements
Highlights
Introduction to solid geometry drawing with orthographic projection techniques.
Explanation of drawing the front, top, and right views of a geometric shape, including sectioned views.
Detailed measurements for a pyramid with a 60Β° angle, length of 75, and side length of 30.
Step-by-step guide on transferring measurements to an auxiliary view for accuracy.
Importance of labeling auxiliary views for clarity and ease of drawing.
Technique for drawing lines and using a 45Β° angle to assist in creating the top view.
Using the middle line for accurate compass measurements to ensure precision in drawing.
Visualization exercise for the top view as if looking down from the top of the pyramid.
Identification of visible and hidden lines in the top view due to the observer's perspective.
Instructions on how to represent cuts in the pyramid and the corresponding solid and dashed lines.
Demonstration of hatching techniques at 45Β° for the top view.
Advice on keeping rulers clean to ensure neatness in drawings, especially during exams.
Introduction to drawing the right view and the observer's perspective from that angle.
Method for transferring points and lines to the right view using the 45Β° line as a reference.
Discussion on the visibility of the base and sides of the pyramid in the right view.
Guidance on incorporating cut lines and solid areas in the right view drawing.
Final touches on the right view, including hatching and adding hidden detail if required.
Note on the availability of grade 11 past papers and the use of matric papers for practice.
Transcripts
okay grade 11 today we are going to be
doing some solid geometry so today we
are going to basically be drawing the
front view which is already on the paper
here top view that is sectioned and the
Right View being sectioned as well okay
so just to quickly go through the
measurements on the paper over here
um the prism so the pyramid is at an
angle of
60Β° okay it's got a length of
75 this has got a side length of 30 this
is your auxiliary view and this is
obviously the front view and then from
this angle here you're going to measure
I believe 40
up okay you're going to measure 30 up no
40 up you're going to bring it across
like that and then it's obviously going
to go through from your 40 points
through to the middle here okay so it
should be self-explanatory if you want
me to do these with you in future draw
these with you guys in future let me
know but let's just get started so
whenever we draw in solid geometry we
always drawing in first orthographic
projection which means we have front top
left and right and 45Β° and 45Β° because
we're drawing the front view top view
and Right View we are using this
orientation here so we've got our front
view which means we're going to have our
top view and our right view over here it
does mean we are going to be drawing
over or having to um
um your raise auxiliary view but you
could always draw each chair um
especially during exams uh draw it where
you don't have to erase it because you
do get marks for your auxiliary views
okay so let's just get started so we're
going to start off by taking the bottom
line here cross like that as well as 10
and 20 just like that over
there okay across like that
and you're going to go across like that
as well what you're then going to do is
from the very last Point here of front
view you're going to draw a
line and you're going to measure 10 and
20 G 10 and 20 just like that and then
you're going to draw lines going up like
this all right once you've done that
you're going to take your
45Β° and you're going to draw a line
going through like that so you can kind
of see um I've still got my auxiliary
view here um just to help me and then
we've got like a grid in the middle so
with the auxiliary view what I like to
do is I like to label it makes things
easier so I'm going to label the top of
the peram T and then we're going to
label the edges so we got one 2 3 four
five and six so if we have to bring
those across that would be 2 three one
and four six and five okay so basically
when drawing the
shape you're are going to bring down
these points um or these lines and they
are going to help get your shape for the
top view so to
start let's take Point T down so it will
be down there 6 and five down it should
go there1 and four down and then
obviously we have already got two and
three down now what I'm going to do is
I'm going to quickly
highlight this line in the middle
here okay the one between our pyramid
and the auxiliary view or the front view
and auxiliary view and then I'm going to
highlight this line here so as you can
both see both these lines are in the
middle because they've got lines on
either side of them and the length of 10
the reason why I point this out is
because it helps keep your measurements
accurate when you're using your compass
so for instance let's just bring these
measurements onto these lines makes
things easier so you're going to bring
all of your measurements
or your points back onto the middle line
like this over here okay so you can
obviously see it touches one two three
okay so we got three points so say now
we want to get point three you're going
to put your compass on that line over
there you're going to measure 2.3 just
like this over
here you're then going to put it on the
blue line again and make a mark and then
you're going to say that's 3 we know 0
five and three will obviously be the the
same so if you want you don't have to
keep measuring your campass you can just
put it on six and five line make your
points and add right five the same with
uh six and two they will be the same
measurements so if we just grab the next
one so say now we grab 6 we know it will
be the same as 2
lengthwise so we're going to put 6 there
and 2 over there but do you see how we
still keep measuring from the blue line
and the blue line so this will two and
six and then we're going to do our last
three measurements so we'll have four
which will be from this point straight
onto this line here okay and then we're
going to measure Point T so that's the
middle point right over here that's C
let's do that again sorry do you see why
we measure on the blue line CU I took
the wrong
measurements okay Point t Blue Line
making
points okay and then we're going to grab
the last points at0
one and that should be from the blue
line right over there okay so before we
get started what I would like to point
out is that because we are now drawing
the top view I want you to imagine that
you are a little man standing on top of
this pyramid here and you are looking
down what are you not going to see okay
okay the first thing we know we are not
going to see is the bottom of this
pyramid right because he's seeing that
but he's not going to see what's
happening underneath which is happening
here so we know that you'll see the
first part of the pyramid which will be
3 four actually make these lines light
I'm making them a bit dark by accident
okay and then he won't see what's
whatever is happening at the back so
these will become Dash lines and I'm
just doing this to help you
visualize um why how we do all of these
things okay we know then that you'll see
one and T okay because it's part of the
per prism that he's going to see we know
that he'll see permid sorry I don't know
why I keep swapping he'll see T2 he'll
see T3 and the little man will also see
T4 so what he won't see though is T5 so
that will be a dash
line and you also want C T6 I mention
this because there are times where you
are going to have to show hidden detail
sometimes you don't sometimes you do but
it's good to know what's going to be
your hidden detail what's not going to
be your hidden detail okay so now what
we're going to do is we're going to cut
it so we know that this pyramid gets cut
at T6 and T5 so we're going to take that
point we're going to find T6 and T5
which end up being these two points that
we here then it cuts at T1 and T4 so
we're going to find T1 and T4 for the
these points over here and then it cuts
right at two and three so we'll have a
cut here so what I'm going to do is I'm
actually going to highlight where the
cut is so that you can see it better and
then we again going to have to make the
rest of the drawing solid that is not
being cut so got a line there have a
line
here a line over there
like
that that and like that okay and then
remember whenever you hatch you hatching
45Β° at equal intervals I'm going to
freehanded please do not do that at all
I'm just doing it so that you guys can
see where things are supposed to be
without wasting too much
time okay so there we've got our cut now
we have to establish what we are going
to see we know that the top Point here
gets cut off so we're not going to see
that anymore but we will still see the
bottom Wing here as well as this point
over here okay and we will see T 21
sorry and this point over here the rest
we won't see the rest will be hidden
detail so when you do draw your stuff
remember your cut must be solid okay so
I'm just going to go over it so you guys
can kind of see what I mean your cut
needs to be solid and then your hatching
needs to be lighter than your solid
drawing okay that's the top view done
which is easy easy peasy okay another
side note I would like you guys to just
remember is you see these little like
smudges on my um paper over here that is
from having dirty rulers so the more you
use them the more there's like stuff
that gets stuck on them like if you rub
your finger across if I do it you can
see it's going like
Gray from all of this stuff on here so
clean your rulers especially during exam
season because it will make sure um or
even Test season it just make sure that
your work looks a whole lot neater okay
so now we're going to be drawing the
Right View okay which means our man is
standing over
here and he's looking at this direction
what is he still not going to see the
base he will see T and he will see some
lines so now we're going to keep that in
mind while we draw the
next point or the next shape okay so
we're going to take all of the lines
across first so like T we've going to
take
across two and three we're going to take
across one and four we are going to take
across and six and five we're going to
take across and then what you're going
to do what you basically use your 45Β°
line for let me
actually again highlight it so that you
can see where our points land
okay we got that over
there basically what you're going to do
is you're going to take your points onto
the orange line right which is your 45Β°
line so like Point T we've taken across
once it's on that orange line you're
going to bring it up that will be Point
T which makes sense because T will be
the highest point from the side okay
then we are going to take the next point
across so let's do one okay so we bring.
one across be on the line there so we've
got one which will be over there okay
two and six line up in this case here so
we're going to have two and six on the
same um sort of line so here we've got
two six so now we're going to find line
two line six okay 2 and six let me just
erase this auxiliary view now so that
you guys can actually see what I'm doing
so I'm just going to erase half of it
and this is why I say when you're doing
your exams draw it here so that you do
not get marks deducted it obviously
depends on the orientation of the
drawing but always make sure that you
can properly see your acceler view okay
you don't want to lose silly marks and I
mean they're so easy to get those marks
you don't want to lose them by not
having your view okay my lines are a bit
skew now so it's going to just have to
be that way I guess now we're going to
bring line three and five across which
will bring on to that line there three
five
that's not correct it will be three and
five this line will not be here that
will be line four which will
be right over here okay so again as I
said we are not going to be
seeing the back or the base of the
pyramid but what we will see if you look
here you will see T6 and T5 so we know
those will be sort of solid do not make
and dark but they will be solid which
means we will see
C1 and
four okay and we won't see well maybe we
will see part of
it okay so let's just draw a base in you
will see this part of the base this part
of the base this part of the
base and you will see a little bit of
the rest I don't think you should see it
but since it's so small it's not highly
possible okay there we go so there
you've got that and then obviously we
will have our hidden detail at the back
but now because we are cutting it we
have to bring our cut points across so
we know two and three cut on the point
so we don't have to worry about that now
we have to cut line one and T1 and T4 so
here we are going to cut T1 T4 like that
and then we also have to cut T6 and T5
which will be those points over here
okay I'm going to connect them together
with highlighter again so that you can
[Music]
see where our points
are okay so you'll have this over here
again you're going to hatch it at 45Β°
using a ruler and at equal intervals and
it should look like that okay and then
we know that this top part gets cut off
so what we will see will be at the
bottom over
here okay we part of
that okay and then that will be cut not
cut that will be solid that'll be solid
and then if they do obviously ask for
hidden detail you can put it in like you
like we have got over here let's just do
that in blue so if you had to put any
hidden detail of the stuff you won't see
it would pretty much look like this here
that I'm going to do
quickly okay so do you see the hidden
detail would be at the back
um yeah okay so then we'll have hidden
detail here as well but you won't see it
there okay so that's basically solid
geometry I hope this helped you guys if
you guys need help doing the true face
let me know and I will do it with you
guys I'm not going to do it in in this
video but if you do need help with it
let me know and I'll make another one
where we do the true face okay so I hope
this helped you guys and another thing
to note grade 11s is there aren't really
grade 11 past papers there are some but
um I can only use the ones on the
government website the past papers which
means matric papers so I will have a
look if they've got R 11 papers but if
they don't I
will make the metric paper videos but
specifically let you guys know if there
are videos that are relevant to you and
what you are learning so that it's not
Matrix standard it's like stuff you guys
can do okay so that you guys can also do
some past papers all right so I hope
hope that this helped you
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