Lesson 22: Practice Problems

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.

Write an equation that represents the volume $V$ as a function of the radius $r$ .
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.
Is the graph of this function a line? Explain how you know.

Problem 2 From Unit 6 Lesson 3

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 From Unit 6 Lesson 7

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

A graph with a curved line that rises and falls and goes through (0,0)

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$y$	$3$	$- 1$	$0$	$4$	$5$	$- 1$

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.

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