How do different ratios compare?
Geometry 11.5 & 11.6
You will be able to provide one or more of these skills for your group today…
Measuring Area
Area of a Trapezoid
Graphic Drawings
Calculating Volume
STICK-WITH-IT-NESS
Volume of Spheres
Volume of Cones
Volume of Pyramids
Volumes of Prisms
Finding Patterns
Writing Ratios
Inductive Reasoning
Making Conjectures from Patterns
ROLES:
 RESOURCE MANAGER – Gets supplies, Organizes clean up, Liaison between group and teacher
 FACILITATOR – Get a QS, Reads task card instructions, Watch time to get team finished
 RECORDER/REPORTER – Make sure everyone records info on exit ticket, 4 parts to exit ticket
 TEAM CAPTAIN – Subs for absent roles, Make sure everyone records info into geometry notebooks
 EVERYONE – Needs to complete assigned drawings as indicated in charts, if in a team of three then split
up pictures from missing person
Kruzich 12
How do different ratios compare?
Geometry 11.5 & 11.6
Supplies: Each person needs: one sheet graph paper, pencil, calculator (maybe) and an exit ticket
FINAL PRODUCT: COMPLETE YOUR EXIT TICKET
EXIT TICKET PART 1: Fill in the chart below from your group’s results. Draw both figures on graph paper.
Figure to Draw all in centimeters
Then enlarge all
dimensions by a factor
of…
Let 1cm = 1 graph box
R/R: A circle whose radius is 1
5 times bigger
TC: A right triangle with base
4 and height 3
3 times bigger
RM: A rectangle that is 2 by 3
4 times bigger
Fac: A trapezoid
like this…
2 times bigger
4
3
Write the SIDE ratio
as a fraction
small to big then reduce
Calculate the AREAS.
Write the AREA ratio
as a fraction
small to big then reduce
2
Complete the following statement based on your observations…
Proportional Areas Conjecture: If corresponding sides lengths of two similar polygons or the radii of two circles
compare in the ratio
Kruzich 12
m , then their areas compare in the ratio _____.
n
How do different ratios compare?
Geometry 11.5 & 11.6
EXIT TICKET PART 2: Fill in the chart below from your group’s results. Draw both figures on graph paper.
Figure to Draw –
all in centimeters
Then enlarge all
dimensions by a factor
of…
R/R: A square based pyramid
whose  height is 4 & the
base sides are 3 cm
2 times bigger
TC: A sphere with radius of 4
5 times bigger
RM: A cone whose radius is 3 &
 height is 4.
3 times bigger
Write the SIDE ratio
as a fraction
small to big then reduce
Calculate the VOLUMES.
Write the Volume ratio
as a fraction
small to big then reduce
Fac: A rectangular prism
whose dimensions are
4 times bigger
2 by 3 by 4.
Complete the following statement based on your observations.
Proportional Volumes Conjecture: If corresponding edge lengths (or radii or heights) of two similar solids
compare in the ratio
m , then their volumes compare in the ratio _____.
n
TEACHER CHECK IN HERE!!
 Check in before you write the formula in your geometry notebook to make sure they are correct.
 Next everyone should copy the formulas from above in your GEOMETRY NOTEBOOK as Conj C-96 and 97.
 You should draw some pictures with numbers to go with the formulas.
Kruzich 12
How do different ratios compare?
Geometry 11.5 & 11.6
EXIT TICKET PART 3: PREDICTION TIME and USING YOUR CONJECTURES (Like tonight’s HW)
Solve the following problems. Write your answer as a decimal approximation to 3 decimals.
1. The ratio of the lengths of corresponding edges of two similar triangular prisms is 5:4.
 What is the ratio of their surface areas?
 What is the ratio of their volumes?
2. The ratio of the volumes of two similar pentagonal prisms is 1:8.
 What is the ratio of their heights?
 What is the ratio of their surface areas?
3. If you need 3 oz of shredded cheese to cover a medium 12 in. diameter pizza, how much shredded cheese
would you need to cover a large 16 in. diameter pizza?
4. The diameter of a soccer ball is about 8.75 in. and the diameter of a tennis ball is about 2.5 in.
 How many times more surface material is needed to make the outside of a soccer ball than a tennis
ball?
 How many times more air does a soccer ball hold than a tennis ball?
Kruzich 12
How do different ratios compare?
Geometry 11.5 & 11.6
EXIT TICKET PART 4: Fill in the chart below from your group’s results. Draw both figures on graph paper.
FIND OUT WHAT HAPPENS IF YOU ONLY DILATE SOME DIMENSIONS…
(You could see this type of thing on the EOC!!)
Figure to Draw –
all in centimeters
Then enlarge ONLY
the following…
R/R: A square whose side
lengths are 2 cm
Double ONE set of
opposite sides
Triple ONE set of
opposite sides
Double only the
HEIGHT
Triple only the
RADIUS
TC: A rectangle that is 3 by 5
RM: A cylinder with radius 2
&  height 4
Fac: A cone whose radius is 2
&  height is 4
Dimension Ratios
are…
Write the indicated ratio
as a fraction
small to big then reduce.
1:1 and 1:2
AREA Ratio =
1:1 and 1:3
AREA Ratio =
1:1 and 1:1 and 1:2
VOLUME Ratio =
1:1 and 1:3 and 1:3
VOLUME Ratio =
What does your group notice about these results? ______________________________________________________
Why do you think this happened differently than before? _______________________________________________
Kruzich 12