Lesson 22
Scaling Two Dimensions
Let’s change more dimensions of shapes.
Problem 1
There are many cylinders with a height of 18 meters. Let \(r\) represent the radius in meters and \(V\) represent the volume in cubic meters.
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Write an equation that represents the volume \(V\) as a function of the radius \(r\).
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Complete this table, giving three possible examples.
\(r\) \(V\) 1 -
If the radius of a cylinder is doubled, does the volume double? Explain how you know.
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Is the graph of this function a line? Explain how you know.
Problem 2
As part of a competition, Diego must spin around in a circle 6 times and then run to a tree. The time he spends on each spin is represented by \(s\) and the time he spends running is \(r\). He gets to the tree 21 seconds after he starts spinning.
- Write an equation showing the relationship between \(s\) and \(r\).
- Rearrange the equation so that it shows \(r\) as a function of \(s\).
- If it takes Diego 1.2 seconds to spin around each time, how many seconds did he spend running?
Problem 3
The table and graph represent two functions. Use the table and graph to answer the questions.
![A coordinate plane, x, 0 to 14 by ones, y, negative 4 to 4.](https://cms-im.s3.amazonaws.com/Zyr3x7CZP4YJBJBVozkSBWqS?response-content-disposition=inline%3B%20filename%3D%228-8.5.B7.PP.Image.103.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.B7.PP.Image.103.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162131Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fa134413911a07ed34225051b0f0bdc9efb436c14504b814e2d16ed1e18899d2)
\(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
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\(y\) | 3 | -1 | 0 | 4 | 5 | -1 |
- For which values of \(x\) is the output from the table less than the output from the graph?
- In the graphed function, which values of \(x\) give an output of 0?
Problem 4
A cone has a radius of 3 units and a height of 4 units.
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What is this volume of this cone?
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Another cone has quadruple the radius, and the same height. How many times larger is the new cone’s volume?