IM 8.5.18 Lesson: Scaling Two Dimensions
, , , , and all represent positive integers. Consider these two equations: and Which of these statements are true? Select all that apply.
Create a true statement of your own about one of the equations.
Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base s. She asks Han what he thinks will happen to the volume of the rectangular prism if she triples s.
Han says the volume will be 9 times bigger. Is he right? Explain or show your reasoning.
A cylinder can be constructed from a piece of paper by curling it so that you can glue together two opposite edges (the dashed edges in the figure).
If you wanted to increase the volume inside the resulting cylinder, would it make more sense to double , , or does it not matter?
If you wanted to increase the surface area of the resulting cylinder, would it make more sense to double , , or does it not matter?
How would your answers to these questions change if we made a cylinder by gluing together the solid lines instead of the dashed lines?
There are many cones with a height of 7 units. Let represent the radius and represent the volume of these cones. Write an equation that expresses the relationship between and . Use 3.14 as an approximation for .
Predict what happens to the volume if you triple the value of .
Graph this equation.
What happens to the volume if you triple ? Where do you see this in the graph? How can you see it algebraically?
Where do you see this in the graph?
How can you see it algebraically?