Setting up an inequality with absolute value

[bnosam]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

Any hints would be great

 

[berkeman]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

Any hints would be great

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.

 

[bnosam]

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.

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

 

[berkeman]

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

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%?

 

[bnosam]

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%?

A cube root?

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

Like that?

 

[SammyS]

A cube root?

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

Like that?

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 [itex]\ x=\sqrt[3]{216\,}=6\,\text{cm}/ .[/itex]

So basically you need to solve

[itex](6+\Delta x)^3=216+2.16=218.16[/itex]

and [itex]\ \ (6+\Delta x)^3=216-2.16=213.84\ [/itex]​

for Δx .

 

[bnosam]

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 [itex]\ x=\sqrt[3]{216\,}=6\,\text{cm}/ .[/itex]

So basically you need to solve

[itex](6+\Delta x)^3=216+2.16=218.16[/itex]

and [itex]\ \ (6+\Delta x)^3=216-2.16=213.84\ [/itex]​

for Δx .

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"

 

[berkeman]

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"

And the the absolute valueaspect is probably involved by this:

|+/- x| = ?