IM 8.5.21 Lesson: Cylinders, Cones, and Spheres

Four students each calculated the volume of a sphere with a radius of 9 centimeters and they got four different answers.
[list][*]Han thinks it is 108 cubic centimeters.[/*][*]Jada got [math]108\pi[/math] cubic centimeters.[/*][*]Tyler calculated 972 cubic centimeters.[/*][*]Mai says it is [math]972\pi[/math] cubic centimeters.[/*][/list]Do you agree with any of them?
Explain your reasoning.
The volume of this sphere with radius r is V = 288π.
[img]data:image/png;base64,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[/img][br][br]This statement is true: [math]288\pi=\frac{4}{3}r^3\pi[/math][br][br][br] What is the value of [math]r[/math] for this sphere? Explain how you know.
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
[table][tr][td]If your teacher gives you the [i]problem card[/i]:[/td][td]If your teacher gives you the [i]data card[/i]:[/td][/tr][tr][td][list=1][*]Silently read your card and think about what information you need to be able to answer the question.[/*][*]Ask your partner for the specific information that you need.[br][/*][*]Explain how you are using the information to solve the problem.[br]Continue to ask questions until you have enough information to solve the problem.[br][/*][*]Share the [i]problem card [/i]and solve the problem independently.[br][/*][*]Read the [i]data card[/i] and discuss your reasoning.[br][/*][/list][/td][td][list=1][*]Silently read your card.[/*][*]Ask your partner [i]“What specific information do you need?”[/i] and wait for them to [i]ask[/i] for information.[br]If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.[br][/*][*]Before sharing the information, ask “[i]Why do you need that information?[/i]” Listen to your partner’s reasoning and ask clarifying questions.[br][/*][*]Read the [i]problem card[/i] and solve the problem independently.[br][/*][*]Share the [i]data card[/i] and discuss your reasoning.[br][/*][/list][/td][/tr][/table][br]Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.[br][br]Use this space to take notes during the activity.
A cylinder with diameter 3 centimeters and height 8 centimeters is filled with water.
[img]data:image/png;base64,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[/img][br]Decide which figures described here, if any, could hold all of the water from the cylinder.
For each of the figures from above, explain your reasoning.
A thirsty crow wants to raise the level of water in a cylindrical container so that it can reach the water with its beak.[br][list][*]The container has diameter of 2 inches and a height of 9 inches.[/*][*]The water level is currently at 6 inches.[/*][*]The crow can reach the water if it is 1 inch from the top of the container.[/*][/list][br]In order to raise the water level, the crow puts spherical pebbles in the container. If the pebbles are approximately [math]\frac{1}{2}[/math] inch in diameter, what is the fewest number of pebbles the crow needs to drop into the container in order to reach the water?

IM 8.5.21 Practice: Cylinders, Cones, and Spheres

[size=150]A scoop of ice cream has a 3-inch diameter. How tall should the ice cream cone of the same diameter be in order to contain all of the ice cream inside the cone?[/size]
[size=150]Calculate the volume of the following shape with the given information. Give each answer both in terms of [math]\pi[/math] and by using [math]3.14[/math] to approximate [math]\pi[/math]. Make sure to include units.[/size][br][br]Sphere with a diameter of 6 inches
Cylinder with a height of 6 inches and a diameter of 6 inches
Cone with a height of 6 inches and a radius of 3 inches
How are these three volumes related?
[size=150]A coin-operated bouncy ball dispenser has a large glass sphere that holds many spherical balls. The large glass sphere has a radius of 9 inches. Each bouncy ball has radius of 1 inch and sits inside the dispenser.[br][br][/size]If there are 243 bouncy balls in the large glass sphere, what proportion of the large glass sphere’s volume is taken up by bouncy balls? Explain how you know.
[size=150]A farmer has a water tank for cows in the shape of a cylinder with radius of 7 ft and a height of 3 ft. The tank comes equipped with a sensor to alert the farmer to fill it up when the water falls to 20% capacity. What is the volume of the tank be when the sensor turns on?[/size]

Information