7th Grade Mathcalbomath.weebly.com/.../g8_u4_cylinderconesphere.docx · Web view5. Kimberly purchased an ice cream cone, represented in the diagram below. She was curious – she
8
Name: 11/17/14 Math 804 OWNCS Aim:_______________________________________________________________________ _______________ CYLINDERS CONES SPHERES
To understand and apply the formulas for cylinders, cones, and spheres.
Jeff Li, 04/14/13,
This one will be the trickiest…2/3 * pi-rsquared… will be the half-sphere. What will be the whole sphere?Twice that… or 4/3 pi-rsquared*hBut what is the height? (have kids turn and talk)… it’s the same as the radius!4/3*pi*r-cubed, not squared
Jeff Li, 04/14/13,
In the space next to it, talk about how you can fit three of these in here… so the formula is the same, *1/3
Jeff Li, 04/14/13,
Use quarters to illustrate this… use one quarter – talk about the area (pi*r-squared)Stack 8 quarters on top of one another… what would be the volume of this? (8*pi*r-squared)V = pi*r-squared*h
EX AMPLE 1 Cynthia would like to buy a new vase to keep fresh flowers in her apartment. Since she is so busy, she would like to buy a vase that holds a lot of water. She is deciding between the three options below that she found on a website.
The cylinder has a diameter of 10 cm and a height of 40 cm. The cone has a base diameter of 16 cm and a height of 45 cm. The sphere has a diameter of 18 cm.
If she wants to buy the vase with the most water, which should Cynthia buy?
Jeff Li, 04/15/13,
This example allows us to practice each of the formulas in a single problem.For each one, ensure that kids write down the formulas, then write down the formulas with substitution, and then use the calculators to figure them out. In an organized way… and label each “cylinder,” “cone,” and “sphere”Use pi button for pi, NOT 3.14… (NYS regs)Walk kids through using the scientific calculators on this one… using the doc camDo not use the calculator until the formula is fully written
EXA MPLE 2
Jeff Li, 04/15/13,
Draw special attention to the diameter of 12 inches… in fact, it could be good to make a “mistake” on purpose and use 8 in the formula for the cylinder to see if kids catch it…
BRONZE1.
2.
3.
Jeff Li, 04/15/13,
Might be good to get kids started… what is the radius of the base of this cylinder?
4.
SIL VER 5. Kimberly purchased an ice cream cone, represented in the diagram below. She was curious – she wondered if the entire volume of the ice cream (the sphere) could fit completely inside the cone.
Is the volume of the cone great enough to fit all of the ice creeam? Show your work.
GOLD6.
Jeff Li, 04/15/13,
Review this one in the huddle
Jeff Li, 04/15/13,
Review this one quickly in huddle – what is the radius of this sphere?
7. Explain why each of the formulas works the way it does in the table below.
FIGURE VOLUME FORMULA EXPLAIN THE FORMULACylinder
Cone
Sphere
THE ANSWERS1. C
Jeff Li, 04/15/13,
Share a few kids’ work with doc cam on this one… push them to explain why the formulas are the way they are….:)
2. D
3. C
4. B
5. The volume of the sphere of ice cream is 65 cm3. The volume of the cone is 72 cm3. Therefore, yes,
