Finding Cylinder Dimensions
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to get students thinking about the structure of the volume formula for cylinders as preparation for the work in the rest of the lesson (MP7). Previously, students were given enough information to determine the radius and the height of a cylinder before calculating its volume. Here, students are given information to find the area of the cylinder’s base, but they are not given the height. An important takeaway is that any positive value for the volume is possible given the right height.
Launch
Arrange students in groups of 2. Remind students of the display of the volume formula for a cylinder created in a previous lesson. Give students 1–2 minutes of quiet work time followed by time to explain their reasoning to their partner. Follow this with a whole-class discussion.
Student Task
What is a possible volume for this cylinder if the diameter is 8 cm? Explain your reasoning.
Sample Response
Sample response: The radius of the cylinder’s base is 4 cm, which means the area of the base is 16π cm2 since 42⋅π=16π. If the height is 1 cm, then the volume would be 16π cm3 since 16π⋅1=16π.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to see how the height of a cylinder is related to its volume.
Invite 2–5 groups in which partners had very different values for the volume of the cylinder to share. Record and display the dimensions and volumes of cylinders that correspond to solutions given by students to show the range of possible volumes. For example, if one student picked h=0.5, while the other picked h=100, the volumes of the two resulting cylinders are quite different even though they each have the same area for their bases.
Anticipated Misconceptions
- “Tell me more about what you know about this cylinder.”
- “How could the formula for the volume of a cylinder help you?”
Standards
- 8.G.9·Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 8.G.C.9·Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
15 min
15 min
Knowledge Components
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Finding Cylinder Dimensions
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to get students thinking about the structure of the volume formula for cylinders as preparation for the work in the rest of the lesson (MP7). Previously, students were given enough information to determine the radius and the height of a cylinder before calculating its volume. Here, students are given information to find the area of the cylinder’s base, but they are not given the height. An important takeaway is that any positive value for the volume is possible given the right height.
Launch
Arrange students in groups of 2. Remind students of the display of the volume formula for a cylinder created in a previous lesson. Give students 1–2 minutes of quiet work time followed by time to explain their reasoning to their partner. Follow this with a whole-class discussion.
Student Task
What is a possible volume for this cylinder if the diameter is 8 cm? Explain your reasoning.
Sample Response
Sample response: The radius of the cylinder’s base is 4 cm, which means the area of the base is 16π cm2 since 42⋅π=16π. If the height is 1 cm, then the volume would be 16π cm3 since 16π⋅1=16π.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to see how the height of a cylinder is related to its volume.
Invite 2–5 groups in which partners had very different values for the volume of the cylinder to share. Record and display the dimensions and volumes of cylinders that correspond to solutions given by students to show the range of possible volumes. For example, if one student picked h=0.5, while the other picked h=100, the volumes of the two resulting cylinders are quite different even though they each have the same area for their bases.
Anticipated Misconceptions
- “Tell me more about what you know about this cylinder.”
- “How could the formula for the volume of a cylinder help you?”
Standards
- 8.G.9·Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- 8.G.C.9·Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.