# Lesson 6 Towers and Cylinders Solidify Understanding

## Learning Focus

Analyze contexts to identify the key features of an inverse variation.

What do I look for to claim that a relationship is an inverse variation in a table, a graph, or an equation?

## Open Up the Math: Launch, Explore, Discuss

Mateo’s little sister, Maria, is building towers out of

### 1.

List all possible combinations of tower height and area of the base that Maria can make with her

Possible tower combinations:

Maria’s tower problem reminds Mateo of some of the work he has done in chemistry class measuring liquids with cylindrical beakers. For small amounts of liquid, he has noticed that narrower cylinders work better, since the markings on the side of the beaker are farther apart than they are on fatter beakers, allowing for more precise measurements. Mateo recalls a recent experiment in which he needed to measure out

### 2.

How would Mateo’s graph of the relationship between height of the liquid and area of the base of the cylinder compare to Maria’s graph representing her towers?

Mateo would like to examine the relationship between the height of liquid in a cylinder and the radius of the base. He wonders if this is also an inverse variation.

### 3.

Complete this table, graph, and equation for Mateo’s relationship between the height of liquid in a cylinder and the radius of the base for

Table:

Equation:

Graph:

### 4.

Is the relationship given by the representations in problem 3 an inverse variation? What is similar and what is different between the way the height of the liquid varies with relationship to the independent variable, area, or radius, as described in problems 2 and 3?

### 5.

Modify the table you created in problem 3 to be a relationship between the quantities

## Ready for More?

Why is it not sufficient evidence to say that a graph represents an inverse variation by observing characteristic trends, such as noting that as the input quantity gets large, the output quantity approaches

## Takeaways

The volume formulas for the volume of a right rectangular prism,

This form reveals

To find an inverse or direct variation relationship,

## Lesson Summary

In this lesson, we continued to explore inverse variation functions in geometric contexts and found that we may need to strategically choose the quantities related by a function in order to reveal a potential inverse variation relationship. We also learned to be careful when examining the shape of a graph as potentially displaying an inverse function relationship.

### 1.

What does it mean to have a

Probability is the measure of how likely an event will occur. Probabilities are written as fractions or decimals from

Write not possible, unlikely, as likely as not, likely, or certain to describe each event. The following scale might help you think about your answers.

#### a.

You were once

#### b.

You have taken four tests in math this term and have earned scores of

#### c.

Next week will have three Mondays.

### 2.

Solve for