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How to solve this.
A cylinder of length 2x is inscribed in a sphere of radius a . Between one end ot this cylinder & sphere, another cylinder is inscribed with one end on an end of the first cylinder so that the axes of the cylinders are collinear. Show that the sum of the volumes of the two cylinders is,
V= 2(Pi) ( x + y )^( a^2  x^2  4y)
Thanks
 2 years ago
 2 years ago
How to solve this. A cylinder of length 2x is inscribed in a sphere of radius a . Between one end ot this cylinder & sphere, another cylinder is inscribed with one end on an end of the first cylinder so that the axes of the cylinders are collinear. Show that the sum of the volumes of the two cylinders is, V= 2(Pi) ( x + y )^( a^2  x^2  4y) Thanks
 2 years ago
 2 years ago

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Shayaan_MustafaBest ResponseYou've already chosen the best response.0
Are you understanding question?
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
This is a hard problem. I think we need Satellite.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
I think maybe. I tried to draw it and that is not easy.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
nothing is hard. we can do anything. just need of help.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Also it would be helpful if we knew what y represents.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
i think coordinates. because he talk about axes. isn't it?
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
first we need a diagram. otherwise it will take more time to understand.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
The axes of the cylinders. So I would assume that means the line down the middle of the cylinder that is perpendicular to both bases.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Or perhaps I am wrong in my assumption that these are right circular cylinders.
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
Tried to figure out the diagram too
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Is there any information as to what y represents?
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
The axes of the cylinders. So I would assume that means the line down the middle of the cylinder that is perpendicular to both bases. Yeah i agree.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
A cylinder of length 2x is inscribed in a sphere of radius a dw:1327783252116:dw Is this right? for the above mentioned line?
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
I think x & y represent the value of r^2
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
So what we need to know now is the radius of the cylinder so that we can find the area of the bases of the cylinder.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
can you elaborate the wording from the word "between one end of this cylinder?" so that we could figure it out.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
So is there some relationship between a sphere and the radius of the circle whose center is ax units from the endpoint of the diameter?
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
I think one end of the cylinder is touching each other
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
@Mertsj. Here is just a sphere not a circle.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
we need some more help. now i want to answer this question.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
But if the cylinder is inscribed in a sphere, isn't the base of the cylinder a circle of the sphere?
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
hmmm... yes you are right. but does this matter here?
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
It can be mean that the cylinder is in lying position
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
yes cbrsam you are right. cylinders are in lying position. therefore their axes are collinear otherwise this is not possible.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
@MertsJ. Are their axes collinear or not?
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
The problem says they are. I need to put another cylinder in my drawing but I am not good at drawing. Do you want to try?
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
If we see only one cylinders . 2a  2x is the part that protrude out at the end of cylinder
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Actually ax since there is an equal piece at both ends of the cylinder.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
remember guys. axes must be collinear. otherwise we could not be able to find volume.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
What class are you taking. Is this a calculus problem?
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
ax for one side yes it is.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Is it a calculus problem?
 2 years ago

shaan_iitkBest ResponseYou've already chosen the best response.0
okk .. I will approach this as .. the big cylinder (with length 2x) would have radius as sqrt (a^2  x^2) the smaller cylinder would have radius as sqrt(a^2  (x+y)^2) .. this is assuming y is the length of the smaller cylinder ... then if I solve .. i get sum of volume as pie*(a^2 + y^2  x^2)*(y + 2x)
 2 years ago

shaan_iitkBest ResponseYou've already chosen the best response.0
but the answer ain't matchin
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
yes this y is confusing to us.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
@shaan_iitk. I got the same ans. :(
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
is this question complete? may be he forget to give description about y.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Perhaps y is the radius of the small cylinder and it has height 2x since the problem specifies that one end is on the end of the first cylinder.
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
That the question I got nothing else specified. Can it be the second cylinder is the same size
 2 years ago

shaan_iitkBest ResponseYou've already chosen the best response.0
well then the question is incomplete ..isn't it.. there has to be some meaning of y
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
really i am an electronics engineer, solid state physicist, semi conductor physicist, interest in cosmology. but not a good mathematician.
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Could that be what is meant?
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
It stated that the other cylinder only touches one side so it should be outside
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
And it also says that is it inscribed.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
@Mertsj Read line. "Between one end ot this cylinder & sphere", another cylinder is inscribed cylinder and sphere.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
we need another help. until we don't figure it. we can't move ahead.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
not this too. i am sure.
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
I think this is the right diagram
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
So do we agree that the volume of the large cylinder is 2pi(x)(a^2x^2)?
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
kindly review again this line. Between one end ot this cylinder & sphere, "another cylinder is inscribed" another cylinder means the whole other cylinder. can't see it? huh.
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
Let try. First take vol of sphere vol of fist cyl. We got 4 equal outer region that does not touch the cyl
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
ok try. i will just see.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
will any one try to solve it?
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
\[V=2\pi x(a ^{2}x ^{2})\] Volume of first cylinder
 2 years ago

Jemurray3Best ResponseYou've already chosen the best response.0
It'd be lovely to have a definitive answer of what y is still... :)
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
hmm... may be you are right Mertsj. this seems to be the volume of the first cylinder.
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
yes this y creating confusion. still.
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
What I get is v = 4 Pi. ( a x )^2
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
Let y be the distance that the small cylinder extends below the large cylinder. Then the height of the small cylinder is y+2x and the radius of the small cylinder is a^2(y+x)^2 and it's volume is pi(y+2x)[(a^2(y+x)^2]^2
 2 years ago

MertsjBest ResponseYou've already chosen the best response.0
And the total volume of the two cylinders is \[2\pi x(a ^{2}x ^{2})+\pi (y+2x)[a ^{2}(y+x)^{2}]^{2}\]
 2 years ago

Jemurray3Best ResponseYou've already chosen the best response.0
Where did this problem come from? I would be willing to nearly bet my life that there is some indication of what y is supposed to be in the problem, variables are never implicitly defined like that.... additionally, could we get a clarification on the correct answer? Because dimensionally what's typed in the box can't be right, so was there a typo, or what?
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
That was the question given to me
 2 years ago

Jemurray3Best ResponseYou've already chosen the best response.0
In that case, I would ask you to clarify these questions with the source.
 2 years ago

accessibmBest ResponseYou've already chosen the best response.0
It says the 2 cylinder are collinear. Thus, I think both the drawings are incorrect?
 2 years ago

Shayaan_MustafaBest ResponseYou've already chosen the best response.0
yes. i agree with accessibm. That is what i am also saying.
 2 years ago

accessibmBest ResponseYou've already chosen the best response.0
Volume of first cylinder =2πX(a^2−x^2) this looks fine. if we confirm the vol of 1st cylinder is as above. we can substract from the sum of vol. which gives us the vol of the 2nd cylinder. perform some reverse engineering and hopefully get some ans? so far cannot conclude any ans. maybe there is typo error in the sum of the vol. stated in the question. Do confirm.
 2 years ago

cbrsamBest ResponseYou've already chosen the best response.1
Hi Mertsj, shayaan, accessibm, Jemurray already check with the source, there is some mistake in the question. The 2nd cylinder is of length 2y is inscribed. The equation is V= 2(Pi) (x+y) (a^2  x^2 4y ) Thanks
 2 years ago

accessibmBest ResponseYou've already chosen the best response.0
Then the vol of the sm cyl will be 2πY(a^2−(X+2Y)^2). add both vol. Still dont not add up to the eqn. Do confirm if there is typo error? I believe the approach is correct. The diagram should look like a urn in a sphere from 2D front view.
 2 years ago
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