Measurement & Modeling
Modules 18, 19, and 20
QOD # 51
35 Minute Movie!!!!
FLAT LAND
Adapted from a book
by: Edwin A. Abbott
Nets,Cross Sections, Rotations
module 19
GOALS:
**I can draw and identify nets & cross sections of 3D solid figures
→ I can:
Identify the most precise name for each pictured solid:
Euler’s Formula
Cube
Rectangular Prism
Triangular prism
Square pyramid
Cone
Cylinder
What is a net?
A net is a two-dimensional pattern of a three-dimensional solid
Match the solid to the correct Net on the right.
optional Project - Nets
Visit
Pick a character, (more than a single cube) and print out the net. card stock works best….but is not required. If you don’t have color print as an option, color your character before you cut it out and put it together. Difficulty level will be taken into account.
Cross Sections (Cylinder):
Cross Sections (Square Pyramid)
CONE
Cross Sections of a Cone
Triangle
Cross Section of a Sphere
Which letter represents the cross section of a sphere?
Rotation Questions
a
b
c
d
optional Project - Nets
Visit
Pick a character, (more than a single cube) and print out the net. card stock works best….but is not required. If you don’t have color print as an option, color your character before you cut it out and put it together. Difficulty level will be taken into account.
Evaluate the total volume of the compound figure:
QOD #52
VOLUME
Module 18
The amount of space measured in cubic units that an object or substance occupies
GOALS:
→ I can:
Volume of �Prisms, Cylinders, Pyramids, Cones, and Spheres.
Prisms and Cylinders
Module 18.1
Volume of a Prism
V = Bh
B = area of Base
h = height of prism
rectangular prism
Example:
Finding Volume of Non-rectangular Prisms
V = Bh
Evaluate Volume
Evaluate Volume
Evaluate Volume
Evaluate Volume
Reminder: Area of Regular Polygons
(Perimeter of a regular polygon equals a side length times the number of sides, by the way)
8 cm
Evaluate Volume
Evaluate Volume
Volume of a Right Cylinder
V=Bh
r = radius
B = Area of circle base
h = height
Circle Formulas you need to know:
Evaluate the circumference and area of the circle to the right if the diameter is 14cm.
Evaluate Volume
5
3
2
6
20
5
4
Solve for Volume of each figure:
TNReady
Volume =
Volume of a Right Pyramid
B = area of base
h = height
h
Why ⅓ ?
Examples:
Solutions
Solutions
Volume of a Cone
h
Volume of Sphere
r = radius
Volume of hemisphere
Evaluate the volume of each figure
Evaluate the total volume
Go back to QOD #52 and solve what can!
QOD #53
Evaluate total volume:
4in
10in
10in
20 in
VOLUME
Module 18
The amount of space measured in cubic units that an object or substance occupies
GOALS:
→ I can:
Volume of Sphere
r = radius
Volume of hemisphere
Evaluate the volume of each figure
Volume Problems
On a separate sheet of paper, show the work (steps a-e) on finding volume of each figure.
#7 requires some perseverance! - Honors Level
#7
Solutions
Half a sheet of paper with somebody
Will it overflow?
1. How many meatballs will it take to overflow?
2. What is a number of meatballs you know is too high?
3. What is a number of meatballs you know is too low?
What information would be useful?
What does the math say?
The answer!
QOD #54
Evaluate the total volume; Leave answer in terms of pi.
VOLUME
Module 18
The amount of space measured in cubic units that an object or substance occupies
GOALS:
→ I can:
TN Ready
Solutions
Assignment:
l
l
h
As you enter the classroom:
It’s going to be a good day :)
-Mrs. B
�QOD # 55
Evaluate total surface area of the composite figure.
Surface Area
module 19
GOALS:
**I can evaluate Surface Area of 3D solid figures
→ I can:
On a sheet of paper (that you will be turning in):
Evaluating Surface Area Task
Evaluating Surface Area Task
Surface Area Findings
Surface Area Findings
Surface Area Findings
QOD #56 Find Surface Area
Take out your volume and surface area problems 1-9
Surface Area
module 19
GOALS:
**I can evaluate Surface Area of 3D solid figures
→ I can:
Lateral Area of a Right Prism
P = perimeter
h= height
Surface Area of a Right Prism
You can find the surface area of a prism by adding the areas of each of the faces.
LA = Lateral Area
P = perimeter, h = height,
B= area of base
LA=ph
S.A. = ph + 2B
S.A. = ph + 2B
Evaluate Surface Area
Lateral Area of a Right Cylinder
Surface Area of a Right Cylinder
h = height, r = radius of base
Heights of a Pyramids & Cones
vertex
slant
height
slant height (l) – the height of each
lateral face
altitude (h) – the segment from the
vertex perpendicular to the base
Pyramids
l = slant height
P = perimeter of base
Lateral Surface Area:
Total Surface
Area
B = area of base
Cones
Lateral Surface Area: Total Surface Area:
r = radius, l = slant height
When a plane intersects a sphere so that it contains the center of the sphere, the intersection is called a great circle.
Each great circle separates a sphere into 2 congruent halves called hemispheres.
SPHERE
Surface Area of Sphere
r = radius
Surface Area of hemisphere
Assignment:
Tutorial video
TURN IN CASTLE SHEETS
TNReady Type Question
QOD Quiz #9
Modeling
Module 20
Goals: I can
Solutions
Solutions
Solutions
TNReady Review
TNReady Warm-Up
Solutions
Evaluate Volume & Surface Area of the figure below:
h
l=
Solutions
TNReady Warm-up
Solutions
Solutions
Solutions
Solutions
Solutions
Solutions
Follow Directions:
Please put Chromebooks away responsibly.