Warm-up SIMILARITY, cont’d New Topics: SOLIDS PRISMS CYLINDERS.
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Warm-up SIMILARITY, cont’d New Topics: SOLIDS PRISMS CYLINDERS Agenda for today
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Transcript of Warm-up SIMILARITY, cont’d New Topics: SOLIDS PRISMS CYLINDERS.
Warm-upSIMILARITY,
cont’d
New Topics:SOLIDSPRISMSCYLINDERS
Agenda for today
Lighthouse – how tall is the real thing if the scale of this model is 1:1200?
Elephant – how tall is the real thing if the scale of this model is 1:120?
Car – come up with the scale based on the actual length of Dodge’s 2005 Charger: 200 inches
Ship’s cannon – come up with the scale based on an actual barrel length of 5 feet
Beaver – If the actual length of Castor canadensis is 2 feet from snout to tip of tail and model length is 2 inches, what is the scale?
Quarters – when the case is open, what is the ratio of area of paper to area of quarters?
Eyeballs – if real human eyes are 1 inch in diameter, what is the scale of the chocolate eyeball model?
Green plastic design tool – draw (and furnish) a room and label the scale factor
Bicycle map – based on the map’s scale, what is the closest that the Willamette River gets to Rocky Butte (as the paper airplane flies)
More…
Triangles are similar if they…
Have the same angle sizes in the same order (AA)
Have corresponding sides whose ratios are equal (SSS)
Have two corresponding sides with the same angle between them (SAS)
FIRST PROBLEM SET
Similar polygons (con't)
Draw similar polygons
Create a scale drawing
Determine whether two polygons are similar or not
SECOND PROBLEM SET
Similar polygonsTASKS
What is the relationship between the size of individual triangles’ interior angles and the sides across from them?
Discussion question
Are 3-dimensional
Some have only polygons for faces and are called polyhedra (singular, polyhedron)
Topic: Solids
Solids (continued)This one is a polyhedron:
Include prisms, pyramids, cylinders, cones, and spheres
Have surface area (units are squared)
Have volume (units are cubed)
Solids (continued)
Examples of different types:
Solids (continued)
Surface area is like…
Volume is like…
Use a formula to find the surface area
Use a formula to find the volume
Correctly label with specific terms
THIRD PROBLEM SET
Solids TASKS
Have 2 identical (congruent) faces (called bases – these lie in parallel planes)
Solids: Prisms
Are named for the shape of their bases
pentagonal prism vs. hexagonal prisms
Solids: Prisms (continued)
Have lateral faces that connect the bases
Are named for the angle of their lateral edges
The lateral edges can be “right” or “oblique”
Solids: Prisms (continued)
What shape are the lateral faces?
pentagonal prism hexagonal prisms
Solids: Prisms (continued)
What shape are the lateral faces for these?
Solids: Prisms (continued)
Solids: Prisms (continued)
Right rectangular prism
Oblique rectangular prism
Classify prisms as right or oblique
Classify prisms based on congruent faces
Label a prism’s bases and lateral faces
Prisms TASKS
“SA” stands for surface area
“LA” stands for lateral area (the sum of the areas of lateral faces)
“BA” stands for base area (use appropriate polygon area formula)
Solids: Prisms (continued)
Solids: Prisms (continued)
• LA is made up of the three yellow lateral faces
• BA is one of the red basesFOURTH PROBLEM SET
“V” stands for volume
“BA” stands for base area (use appropriate polygon area formula)
“H” stands for height (be careful if it’s oblique)
Solids: Prisms (continued)
Solids: Prisms (continued)
BA is from one of thecongruent triangles
H is the distance betweenthe congruent triangles
Solids: Prisms (continued)
BA is from one of the congruent pentagon bases
H is the perpendicular distance betweenthe congruent pentagons
Solids: Prisms (continued)
BA is from one of theTriangular bases
H is the long edge of the brown lateral faces
Label a prism’s lateral faces
Find the surface area of a prism
Find the volume of a prism
FIFTH PROBLEM SET
PrismsTASKS (cont'd)
Have 2 identicalfaces (bases)
The two bases are circles
The two bases lie in parallel planes
Solids: Cylinders
Do not have lateral faces; instead there is one, big rectangle wrapped around connecting the bases
Solids: Cylinders (cont'd)
Recall the formula for SA of a prism
Compare it to our cylinder formula
Solids: Cylinders (cont'd)
Recall the formula for V of a prism
Compare it to our cylinder formula
Solids: Cylinders (cont'd)
Label a cylinder’s height and radius
Find the surface area of a prism
Find the volume of a prism
SEVENTH PROBLEM SET
Cylinders TASKS
Discussion question:Which cylinder makes
a better container?
Solids: Cylinders (cont'd)
