# Setting up an inequality with absolute value

1. Jan 31, 2013

### bnosam

1. The problem statement, all variables and given/known data

I need some help setting up this inequality:
How accurate do the sides of a cube have to be measured if the volume of the cube has to be within 1% of 216 cm^3

Not very good with word problems and for some reason this course never deals with them until now? And this is the first practise question in the chapter on absolute functions.

2. Relevant equations

Not sure, I know it has to contain an absolute value though

3. The attempt at a solution

Any hints would be great

2. Jan 31, 2013

### Staff: Mentor

Why do you think it needs to include an absolute value? When they say 1%, they typically mean within +/- 1%.

Please try to start the problem. We cannot offer tutorial help until you show some effort. That is in the Rules link at the top of the page.

3. Jan 31, 2013

### bnosam

It's part of the practise sheet titled "Absolute value functions" ;) That's what makes me think I need to have it in here.

Well 1% of a 216 is 2.16.

-2.16 < | x | < 2.16

Something like that look fine, I'm not very sure how to set it up at all, that's the best stab at it I could take

4. Jan 31, 2013

### Staff: Mentor

Okay, but it said that is the volume. What tolerance does each side have to have in order for the volume tolerance to be +/- 1%?

5. Jan 31, 2013

### bnosam

A cube root?

$- \sqrt[3]{2.16} ≤ | x | ≤ \sqrt[3]{2.16}$

Like that?

6. Jan 31, 2013

### SammyS

Staff Emeritus
You're taking a shortcut which may or may not be warranted .

Let x be the length of each side of the cube .

If the cube's volume is exactly 216 cm3 , then $\ x=\sqrt[3]{216\,}=6\,\text{cm}/ .$

So basically you need to solve
$(6+\Delta x)^3=216+2.16=218.16$

and $\ \ (6+\Delta x)^3=216-2.16=213.84\$​
for Δx .

7. Jan 31, 2013

### bnosam

The only real issue I kind of have with this is the fact, this needs to contain absolute value because the beginning of the page even says "Solve the following questions containing absolute value problems"

8. Jan 31, 2013

### Staff: Mentor

And the the absolute valueaspect is probably involved by this:

|+/- x| = ?