hhhhhhhhhh

- anonymous

hhhhhhhhhh

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- schrodinger

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- inkyvoyd

Volume of cylinder minus volume of cube

- inkyvoyd

Take the result of that, and divide by volume of cylinder again.

- anonymous

I know how to do it, however I keep doing that and I get different numbers each time. Could you walk me through it?

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## More answers

- inkyvoyd

ok, so we have (pi)*r^2*(h) for the cylinder, but h=2r+4

- anonymous

ok

- inkyvoyd

thus it becomes pi*(r^2)(2r+4)

- inkyvoyd

that's the volume of the cylinder.

- anonymous

makes sense

- inkyvoyd

now a cube is x^3, where x is the length.

- anonymous

x would be r√2

- inkyvoyd

Now, here's the tricky part.

- inkyvoyd

(r√2)^3=2(r^3)√2

- inkyvoyd

{pi*(r^2)(2r+4)-2(r^3)√2} / [pi*(r^2)(2r+4)]
Volume of cylinder

- inkyvoyd

i.e. (Vcylinder-Vcube)/(Vcylinder)

- inkyvoyd

Now, let me write that out, so I don't make a mistake :)

- anonymous

okay : )

- anonymous

your writing ran off the page. I can't see all of it.

- inkyvoyd

This is really confusing; just write it on a piece of paper, it should really help

- inkyvoyd

I canceled out the top and bottom of the Vcylinder to make 1, because it was really the fastest way to do it.

- anonymous

ok one sec.

- inkyvoyd

1-(2(r^3)√2))/(π∗r^2∗(2r+4))
Sorry, it got messed up

- inkyvoyd

{pi*(r^2)(2r+4)-2(r^3)√2} / [pi*(r^2)(2r+4)]
=1-(2(r^3)√2))/(π∗r^2∗(2r+4))

- amistre64

|dw:1333380473049:dw|

- inkyvoyd

The end result I got (may be wrong) is |dw:1333380503250:dw|

- anonymous

ok so why would you do pi*(r^2)(2r+4)^2

- inkyvoyd

In other words, I overly complicated soemthing. :)

- amistre64

area of segment * height = volume of segment cylindar; times 4 equals .... stuff left after cube i think

- amistre64

What fraction of the cylinder's volume is taken up by the other cube?
Vcube/Vcylindar ; whats the "other" cube?

- anonymous

just one cube with the length of r√2

- amistre64

|dw:1333380689297:dw|
is this something like what we are looking at?

- anonymous

THe cube is in the middle but ya

- amistre64

Vcyl = pi r^2 (2r+4) = total
Vcube = r^3 2sqrt(2) = part
part/total = percent

- anonymous

I don't need a percent

- anonymous

Just a fraction

- amistre64

\[\frac{pi\ r^2(2r+4)}{2r^3\sqrt{2}}\to\ \frac{pi\ \cancel{2r^2}(r+2)}{\cancel{2r^3}r\sqrt{2}} \]

- amistre64

percents are fractions

- anonymous

nevermind

- amistre64

i got me top and bottm on the wrong sides; so if you flip it it should be fine

- anonymous

huh?

- amistre64

another way to read the problem is: what percent of the volume is taken up by the cube

- anonymous

ok.

- anonymous

Can someone explain this to me in a non confusing way please?

- anonymous

Meh, got food on the stove, or I'd help you in a possibly easier to understand kind of way..
Focus on writing down formulas for the volume on each object, cylinder and cube. Simplify.

- anonymous

that hasn;t really helped me so far

- anonymous

Type the expressions here, so I see that you got those correct.

- anonymous

What expression? I have been shown so many methods with this question I don't know what I did anymore.

- anonymous

Apply the same logic as "if I slice a pizza in 4 equally large bits, and I then eat 1 slice, in fractions, how much of the pizza have I eaten?".. That would be 1/4.
This is the same logic, the cube occupies (eats) a bit of the cylinders volume, since it's inside the cylinder. The question is, how much? 1/4th? Maybe, we'll find out.
What do we need to find this out? Well, we need to know how large the cylinders total volume is. That's given by the cylinder volume formula, pi*r^2*h. We got both the radius and the height, put them in: pi*r^2*(2r+4)
Then we need the cube right? To find out how much it "eats" of the cylinders volume, we need the cubes volume. We got the length of one side of the cube: r*root2
But that's not the volume, you get the volume by taking the length*3 right? So we get 3(r*root2), so that's how much of the cylinders volume the cube eats. cube volume / cylinder volume. Put them in that fraction, and simplify.

- anonymous

The downside of having multiple people jump at a problem. :)

- anonymous

That is complicating for me.

- anonymous

Indeed GT.. But at least you have 3 different but similar approaches to try and learn from. :P

- inkyvoyd

I have the right answer, ;)

- anonymous

cube volume / cylinder volume = (r*root2)^3 / pi*r^2*(2r+4) = 2r^3r2 / 2r^3*pi(r+2)
Do you understand how I got here kaya? How much have you written down yourself?

- anonymous

I have a form of dyslexia that confuses me with calculator things like sqrt and that sort of thing. I have written down about 3 pages worth of meaning less things for this question

- anonymous

Cylinder volume (total volume) = pi*r^2*(2r+4)
Cube volume (part of the total volume) = (r*root2)^3
part of the volume / total volume = correct answer

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