IM 8.5.17 Lesson: Scaling One Dimension
Here is a graph of the amount of gas burned during a trip by a tractor-trailer truck as it drives at a constant speed down a highway:
At the end of the trip, how far did the truck drive, and how much gas did it use?
If a truck traveled half this distance at the same rate, how much gas would it use?
If a truck traveled double this distance at the same rate, how much gas would it use?
Complete the sentence: ___________ is a function of _____________.
There are many right rectangular prisms with one edge of length 5 units and another edge of length 3 units. Let s represent the length of the third edge and V represent the volume of these prisms.
Write an equation that represents the relationship between [math]V[/math] and [math]s[/math].
Graph this equation.
What happens to the volume if you double the edge length s?
Where do you see this in the graph?
Where do you see it algebraically?
[size=150]There are many cylinders with radius 5 units. Let [math]h[/math] represent the height and [math]V[/math] represent the volume of these cylinders.[/size][br][br]Write an equation that represents the relationship between [math]V[/math] and [math]h[/math]. Use 3.14 as an approximation of [math]\pi[/math].
Graph this equation.
What happens to the volume if you halve the height, [math]h[/math]?
Where can you see this in the graph?
How can you see it algebraically?
Suppose we have a rectangular prism with dimensions 2 units by 3 units by 6 units, and we would like to make a rectangular prism of volume 216 cubic units by stretching one of the three dimensions.
What are the three ways of doing this?
Of these, which gives the prism with the smallest surface area?
Repeat this process for a starting rectangular prism with dimensions 2 units by 6 units by 6 units.
Can you give some general tips to someone who wants to make a box with a certain volume, but wants to save cost on material by having as small a surface area as possible?
Here is a graph of the relationship between the height and the volume of some cones that all have the same radius:
[img]data:image/png;base64,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[/img][br][br]What do the coordinates of the labeled point represent?
What is the volume of the cone with height 5?
What is the volume of the cone with height 30?
Use the labeled point to find the radius of these cones. Use 3.14 as an approximation for [math]\pi[/math].
Write an equation that relates the volume [math]V[/math] and height [math]h[/math].
IM 8.5.17 Practice: Scaling One Dimension
A cylinder has a volume of 48π cubic centimeters and height h. Complete this table for volume of cylinders with the same radius but different heights.
A cylinder has a radius of 3 cm and a height of 5 cm.
What is the volume of the cylinder?
What is the volume of the cylinder when its height is tripled?
What is the volume of the cylinder when its height is halved?
A graduated cylinder that is 24 cm tall can hold 1 L of water.
What is the radius of the cylinder? Recall that 1 liter (L) is equal to 1000 milliliters (ml), and that 1 liter (L) is equal to 1,000 cm[math]^3[/math].
What is the height of the 500 ml mark?
What is the height of the 250 ml mark? [br][br]Recall that 1 liter (L) is equal to 1000 milliliters (ml), and that 1 liter (L) is equal to 1,000 cm[math]^3[/math].
[size=150]An ice cream shop offers two ice cream cones. The waffle cone holds 12 ounces and is 5 inches tall. The sugar cone also holds 12 ounces and is 8 inches tall. Which cone has a larger radius? [/size]
[size=150]A 6 oz paper cup is shaped like a cone with a diameter of 4 inches. How many ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup? [/size]
Lin’s smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged.
When do you think her battery will die?
Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.