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Minimizing the surface of a sphere and cylinder

leprofece

Member
Jan 23, 2014
241
279) A body is formed by a straight circular cylinder which ends up in a hemisphere. What are the dimensions that should have this body so the total surface area is minimal, if your volume is

answer Cubic sqrt( 3V/5 pi)

i tried to post an image of my notes and i couldnot i will type later

Vt = pir2H +2/3piR2 constant
A= 2pirH+ 2pir2

Derive implicit 2piH + pir(dH) + 4pir
dh = (-2r-h)/(r)

derive volume 2pirH + pir2(dH) + 2pir2

2pirH + pir2(-2r-h) + 2pir2 = 0
And I got piRh = 0

So h = 0 and this is not the answer
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: Max and min 6

If the image of your notes is on your hard drive and you are using Windows, you may upload it as an attachment as follows:

1.) Click the imageicon.jpgbutton on the toolbar (you will see "Insert Image" when you hover your mouse cursor over it).

2.) Click the "From Computer" tab.

3.) Click the "Browse" button.

4.) Locate the file on your hard drive (or other available media), then double-click it to select it.

5.) Click "Upload File(s)" and the image will be uploaded and inserted inline in your post.
 

leprofece

Member
Jan 23, 2014
241
Re: Max and min 6

If the image of your notes is on your hard drive and you are using Windows, you may upload it as an attachment as follows:

1.) Click the View attachment 1977button on the toolbar (you will see "Insert Image" when you hover your mouse cursor over it).

2.) Click the "From Computer" tab.

3.) Click the "Browse" button.

4.) Locate the file on your hard drive (or other available media), then double-click it to select it.

5.) Click "Upload File(s)" and the image will be uploaded and inserted inline in your post.
Right I gonna try
NO it appears (! in red)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775

leprofece

Member
Jan 23, 2014
241
Re: Max and min 6

Scan.jpg
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: Max and min 6

279) A body is formed by a straight circular cylinder which ends up in a hemisphere. What are the dimensions that should have this body so the total surface area is minimal, if your volume is

answer Cubic sqrt( 3V/5 pi)

i tried to post an image of my notes and i couldnot i will type later

Vt = pir2H +2/3piR2 constant
A= 2pirH+ 2pir2

Derive implicit 2piH + pir(dH) + 4pir
dh = (-2r-h)/(r)

derive volume 2pirH + pir2(dH) + 2pir2

2pirH + pir2(-2r-h) + 2pir2 = 0
And I got piRh = 0

So h = 0 and this is not the answer
From what I can make out, you are given a body made up of a cylinder inscribed within a hemisphere, and the volume of the two components added together must remain constant. Which measure are you asked to find in terms of this constant volume? The radius of the hemisphere, the radius of the cylinder, or the height of the cylinder.
 

leprofece

Member
Jan 23, 2014
241
Re: Max and min 6

OHH Maybe I forgot to write that R = H
so it is radius and height that are equals to a cubic sqrt= and it is not zero as I found out

R = H = Cubic sqrt( 3V/5 pi)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: Max and min 6

OHH Maybe I forgot to write that R = H
so it is radius and height that are equals to a cubic sqrt= and it is not zero as I found out

R = H = Cubic sqrt( 3V/5 pi)
Does this mean the height of the cylinder must be equal to the radius of the hemisphere? When you post a question, I would ask you to make sure the problem is clearly stated so that we know what you are asking. I am still unclear what you are being asked to do here.
 

leprofece

Member
Jan 23, 2014
241
Re: Max and min 6

Does this mean the height of the cylinder must be equal to the radius of the hemisphere? When you post a question, I would ask you to make sure the problem is clearly stated so that we know what you are asking. I am still unclear what you are being asked to do here.
volume is "V" So it is a problem of max and minimun and i am asked the minimal area of total surface of the body that is the sum of two as you said
 

leprofece

Member
Jan 23, 2014
241
Re: Max and min 6

volume is "V" So it is a problem of max and minimun and i am asked the minimal area of total surface of the body that is the sum of two as you said

Are you still confused ??
Do you want a copy of the spanish problem in your mail ??'
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: Max and min 6

...
Are you still confused ??
Do you want a copy of the spanish problem in your mail ??'
I don't speak or read Spanish, but yes I am still unsure what you are being asked to do. You have not answered my question:

Does this mean the height of the cylinder must be equal to the radius of the hemisphere?
 

leprofece

Member
Jan 23, 2014
241
Re: Max and min 6

Yes According to answer both of them are equals
 
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