# Lesson 22

Scaling Two Dimensions

### 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.

1. Write an equation that represents the volume $$V$$ as a function of the radius $$r$$.

2. Complete this table, giving three possible examples.

$$r$$       $$V$$
1
3. If the radius of a cylinder is doubled, does the volume double? Explain how you know.

4. 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.

1. Write an equation showing the relationship between $$s$$ and $$r$$.
2. Rearrange the equation so that it shows $$r$$ as a function of $$s$$.
3. If it takes Diego 1.2 seconds to spin around each time, how many seconds did he spend running?

### Solution

(From Unit 6, Lesson 3.)

### Problem 3

The table and graph represent two functions. Use the table and graph to answer the questions.

 $$x$$ $$y$$ 1 2 3 4 5 6 3 -1 0 4 5 -1
1. For which values of $$x$$ is the output from the table less than the output from the graph?
2. In the graphed function, which values of $$x$$ give an output of 0?

### Solution

(From Unit 6, Lesson 7.)

### Problem 4

A cone has a radius of 3 units and a height of 4 units.

1. What is this volume of this cone?

2. Another cone has quadruple the radius, and the same height. How many times larger is the new cone’s volume?