anonymous
  • anonymous
hhhhhhhhhh
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
inkyvoyd
  • inkyvoyd
Volume of cylinder minus volume of cube
inkyvoyd
  • inkyvoyd
Take the result of that, and divide by volume of cylinder again.
anonymous
  • 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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inkyvoyd
  • inkyvoyd
ok, so we have (pi)*r^2*(h) for the cylinder, but h=2r+4
anonymous
  • anonymous
ok
inkyvoyd
  • inkyvoyd
thus it becomes pi*(r^2)(2r+4)
inkyvoyd
  • inkyvoyd
that's the volume of the cylinder.
anonymous
  • anonymous
makes sense
inkyvoyd
  • inkyvoyd
now a cube is x^3, where x is the length.
anonymous
  • anonymous
x would be r√2
inkyvoyd
  • inkyvoyd
Now, here's the tricky part.
inkyvoyd
  • inkyvoyd
(r√2)^3=2(r^3)√2
inkyvoyd
  • inkyvoyd
{pi*(r^2)(2r+4)-2(r^3)√2} / [pi*(r^2)(2r+4)] Volume of cylinder
inkyvoyd
  • inkyvoyd
i.e. (Vcylinder-Vcube)/(Vcylinder)
inkyvoyd
  • inkyvoyd
Now, let me write that out, so I don't make a mistake :)
anonymous
  • anonymous
okay : )
anonymous
  • anonymous
your writing ran off the page. I can't see all of it.
inkyvoyd
  • inkyvoyd
This is really confusing; just write it on a piece of paper, it should really help
inkyvoyd
  • 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
  • anonymous
ok one sec.
inkyvoyd
  • inkyvoyd
1-(2(r^3)√2))/(π∗r^2∗(2r+4)) Sorry, it got messed up
inkyvoyd
  • 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
  • amistre64
|dw:1333380473049:dw|
inkyvoyd
  • inkyvoyd
The end result I got (may be wrong) is |dw:1333380503250:dw|
anonymous
  • anonymous
ok so why would you do pi*(r^2)(2r+4)^2
inkyvoyd
  • inkyvoyd
In other words, I overly complicated soemthing. :)
amistre64
  • amistre64
area of segment * height = volume of segment cylindar; times 4 equals .... stuff left after cube i think
amistre64
  • amistre64
What fraction of the cylinder's volume is taken up by the other cube? Vcube/Vcylindar ; whats the "other" cube?
anonymous
  • anonymous
just one cube with the length of r√2
amistre64
  • amistre64
|dw:1333380689297:dw| is this something like what we are looking at?
anonymous
  • anonymous
THe cube is in the middle but ya
amistre64
  • amistre64
Vcyl = pi r^2 (2r+4) = total Vcube = r^3 2sqrt(2) = part part/total = percent
anonymous
  • anonymous
I don't need a percent
anonymous
  • anonymous
Just a fraction
amistre64
  • 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
  • amistre64
percents are fractions
anonymous
  • anonymous
nevermind
amistre64
  • amistre64
i got me top and bottm on the wrong sides; so if you flip it it should be fine
anonymous
  • anonymous
huh?
amistre64
  • amistre64
another way to read the problem is: what percent of the volume is taken up by the cube
anonymous
  • anonymous
ok.
anonymous
  • anonymous
Can someone explain this to me in a non confusing way please?
anonymous
  • 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
  • anonymous
that hasn;t really helped me so far
anonymous
  • anonymous
Type the expressions here, so I see that you got those correct.
anonymous
  • anonymous
What expression? I have been shown so many methods with this question I don't know what I did anymore.
anonymous
  • 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
  • anonymous
The downside of having multiple people jump at a problem. :)
anonymous
  • anonymous
That is complicating for me.
anonymous
  • anonymous
Indeed GT.. But at least you have 3 different but similar approaches to try and learn from. :P
inkyvoyd
  • inkyvoyd
I have the right answer, ;)
anonymous
  • 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
  • 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
  • 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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