Geometry
Semester 2
Unit 5 Lesson 2
18 May, 2016
Agenda 18 May, 2016
Stats test -review Tues
● Volume and Surface Area - Opening Task - review/correct
● Modeling with Geometry 5.1 - quick check and correct
● 5.1 Any Way You Slice it
○ Predicting
○ Trying with modeling clay
○ Areas of triangles
● Volume of Cylinders
● Volume of Pyramid - Demonstration
● Homework
Volume and Surface Area - Opening Task p. 1
To share between 2 people - work together. Be
sensible, please.
“You are given 32….…. cubes and 32……..
cubes and you will put them together to make one
large cube.” Write in the colors you are given edit worksheet based on what you are given to
work with. Use back of sheet, both of you draw &
write in detail.
Volume and Surface Area - Opening Task p. 1
“Find a way to arrange the cubes so that you
maximize the exposed surface that is ----(pick a
color).” you draw & write in detail
All 6
faces
looked
like
this
Volume and Surface Area - Opening Task p. 1
“What percentage of the exposed surface area
will be ----?” you draw & write in detail
1
2
3
4
5
13
14
6
7
15
16
8
9
10
11
12
All 6 faces looked like this
12/16 = ¾ = 0.75 or
75%
Or (12 x 6) = 72 = ¾ = 75%
(16x6)
96
Modeling with Geometry 5.1 pg 2
Ready: Topic Comparing perimeter, area, and volume.
1. Calculate the perimeter of a rectangle that measures 5cm
by 12 cm.
Perimeter = 12cm + 12cm + 5cm + 5cm = 34cm
12cm
5cm
5cm
12cm
Modeling with Geometry 5.1 pg 2
Remember to multiply the units together as well.
2. Calculate the area of the same rectangle
Area = 12cm x 5cm = 60cm2
12cm
5cm
5cm
12cm
Modeling with Geometry 5.1 pg 2
Remember to multiply the units together as well.
3. Calculate the volume of a box that measures 5cm by 12
cm and is 8cm deep
volume = 12cm x 5cm x 8cm = 480cm3
m
8c
12cm
5cm
5cm
12cm
Modeling with Geometry 5.1 pg 2
4. Look back at problems 1 - 3. Explain how the units change
for each answer.
Perimeter is a length the units are cm, for area we multiply 2
lengths together so the units are squared (cm2) and for
volume we multiply 3 lengths together so thecmunits are cubed
8
12cm
3
(cm )
5cm
5cm
12cm
Modeling with Geometry 5.1 pg 2
5. Calculate the surface area for the box, assume it does not
have a lid. “8cm deep” ?
Let’s assume the original rectangle is the “bottom of the box”
12cm
5cm
5cm
12cm
Modeling with Geometry 5.1 pg 2
5. Calculate the surface area for the box, assume it does not
have a lid. “8cm deep” ? One open end if its a box
SA 2 ends = 2 (5cmx8cm) = 80cm2
8cm
8cm
12cm
5cm
8cm
12cm
Modeling with Geometry 5.1 pg 2
5. Calculate the surface area for the box, assume it does not
have a lid. “8cm deep” ?
SA bottom =(5cmx12cm) = 60cm2
8cm
8cm
12cm
5cm
8cm
12cm
Modeling with Geometry 5.1 pg 2
5. Calculate the surface area for the box, assume it does not
have a lid. “8cm deep” ?
SA 2 faces (front and back?) =2(8cmx12cm) = 192cm2
8cm
8cm
12cm
5cm
8cm
12cm
Modeling with Geometry 5.1 pg 2
5. Calculate the surface area for the box, assume it does not
have a lid. “8cm deep” ?
Total SA = 80cm2 + 60cm2 + 192cm2 = 332 cm2
8cm
8cm
12cm
5cm
8cm
12cm
Modeling with Geometry 5.1 page 2
6. Calculate the circumference of a circle if the radius
measures 8 inches. (Use = 3.14).
Circumference = 2 r = 2(3.14) 8in = 50.24 in
7. Calculate the area of the circle in problem 6.
Area = r2 = 3.14(8in)2 = 200.96in2
Modeling with Geometry 5.1 page 2
8. Calculate the volume of a ball with a diameter of 16 inches.
Radius = 8in
Volume of a sphere = 4/3 r3 = 3.14(8in)3 = 2143.57in3
9. Calculate the surface area of the ball in problem 8.
Surface of a sphere = 4 r2 = (4)3.14(8in)2 = 803.84in2
Modeling with Geometry 5.1 page 2
10. I know if a measurement is in inches or cm that it is a
perimeter - because the units are to the power 1. I know an
area unit would be squared - for example, cm2 or in2.
11. In the problems above linear measurements would be the
lengths of edges of a box, or the radius and diameter of a
circle or sphere. Perimeter and circumference are also linear
measurements.
5.1 Any Way You Slice it. Pg 4.
Slice a corner off a cube.
Who followed the instructions?
Precise language to avoid confusion: Cube
Precise language: prisms - base supplies name
Prism - a polyhedron
with 2 congruent
parallel bases
Precise language: prisms - base supplies name
Prism - a polyhedron
with 2 congruent
parallel bases
Precise language: prisms - base supplies name
Prism - a polyhedron with 2 congruent
parallel bases
This is a rectangular prism because the
congruent parallel faces (bases) are
triangles.
(Base - doesn’t mean the face that is flat
on the table)
A cross section is the face formed when a 3D object
is sliced by a plane. It can also be thought of as the
intersection of a plane and a solid.
2. Draw and describe the cross section formed when
Jumal sliced his cube.
3. Draw and describe the cross section formed when
Jabari sliced his cube.
A cross section is the face formed when a 3D object
is sliced by a plane. It can also be thought of as the
intersection of a plane and a solid.
2. Draw and describe the cross section formed when
Jumal sliced his cube.
The cross section would look like a small triangle.
3. Draw and describe the cross section formed when
Jabari sliced his cube.
The cross section would be rectangular.
4. Draw some other possible cross sections that can
be formed when a cube is sliced by a plane.
See if you can find more than one shape for the face of the
cross section.
Share your ideas with your neighbor.
Prepare to share with us all.
Cross Sections of Solids
Horizontal
slice (parallel
to bases)
Vertical
slice
(perpendic
ular to
bases)
Cross Sections of Solids
Angled
slice
(at an
angle to
the bases)
Cross Sections of Solids - make a cube
h
h
Find out what type of
quadrilateral formed by
the intersection of the
plane that passes
through diagonally
opposite edges of a cube
using the dental floss to
slice the modelling clay.
Cross Sections of Solids - make a cylinder
Find out what types of
cross sections you can
make - record your
results on paper (draw
the cylinder, and then all
the different shapes for
cross sections you
make).
Cross Sections of Solids - make a cylinder
Cross Sections of Solids - make a cone
Find out what types of
cross sections you can
make - record your
results on paper (draw
the cone, and then all the
different shapes for cross
sections you make).
Modeling with Geometry 5.1 pg 6
Set
Topic: Cross sections of a cone.
Answer questions 12-15
Go Topic: Area of a triangle
Qu. 17. 18 and 19 count each little
square as 1 unit.
Qu 16. Now try this one according to the markings on the y
axis, each little square is 0.4 units
G. GMD.3 Student NOtes WS #3 Add to the notes
page
The Cylinder
Net for:
G. GMD.3 Student NOtes WS #3 Add to the notes
page
The Cylinder
Net for:
What is the length of the rectangle in the net? The
circumference of the circle that forms the base
base
base
base
base
Becomes curved
Lateral face
G. GMD.3 Student Notes WS #3 Add to the notes page
Cylinder Volume the Stacking Principle
CORRECTION NECESSARY IN BOX
Volume cylinder = Base x height = Bh = B r2
G. GMD.3 Student Notes WS #3 Add to the notes page
Volume cylinder = Base x height = Bh = B r2
G. GMD.3 Student Notes WS #3 Add to the notes page
Volume cylinder = Base x height = Bh = B r2
height
G. GMD.3 Student Notes WS #3 Add to the notes page
Volume cylinder = Base x height = Bh = B r2
Example #1
Height
5cm
r= 4cm
h= 5cm
V = Bh
V= ( r2)h
V= (4cm)25cm
V=80 cm3
G. GMD.3 Student Notes WS #3 Add to the notes page
Volume cylinder = Base x height = Bh = B r2
Diameter =
6cm
Height
4cm
Example #2
Diameter = 6cm
r= 3cm
h= 4cm
V = Bh
V= ( r2)h
V= (3cm)24cm
V= cm3
G. GMD.3 Student Notes WS #3 Add to the notes page
Volume cylinder = Base x height = Bh = B r2
Volume bottom
cylinder +
volume top
cylinder Volume of the
cylindrical hole
through both
Example #3
V = Bh + Bh - Bh
V= (7cm)211cm + (5cm)
2
5cm - (1cm)216cm
V=648 cm3
Homework
Worksheet #3, Pg 16 and 17.
1. a, b, c.
2. a, b, c
3. a, b, c and one other of your choice.
Enrichment today to
complete iReady
Assessment if you had
mandatory iReady
lessons.
Read SE.Pg 20 The Pyramid
Worksheet # 4 pg 22 and 23
1. (all parts) 2. Explain. 3 All parts. 4. And 5. a and b.
6. c and e.