volume of revolution Watch

shelaghglenister
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Help. Can't even visualise the equations I need.

Sphere of radius r where r is greater than 2 has a circular hole drilled completely through so that the axis of the hole is a diameter of the sphere. The hole has length 4. Prove that the volume of the piece of the sphere which remains is independent of r

know y2 = r2 - x2
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TenOfThem
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(Original post by shelaghglenister)
Help. Can't even visualise the equations I need.

Sphere of radius r where r is greater than 2 has a circular hole drilled completely through so that the axis of the hole is a diameter of the sphere. The hole has length 4. Prove that the volume of the piece of the sphere which remains is independent of r

know y2 = r2 - x2
The question does not make sense

If the hole has length 4 and goes all the way through then the radius of the sphere would have to be 2
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shelaghglenister
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(Original post by TenOfThem)
The question does not make sense

If the hole has length 4 and goes all the way through then the radius of the sphere would have to be 2
I am struggling with that, hence why I can't visualise the question. Its from the Neill Quadling text book for Core 3 and 4
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TenOfThem
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(Original post by shelaghglenister)
I am struggling with that, hence why I can't visualise the question. Its from the Neill Quadling text book for Core 3 and 4
Ok

Circle centre 0, radius r

Rotate 180 between -a and a



The only way I can incorporate the 4 is to have a = 2 which makes sense now I have drawn the graph

Then you need to remove the cylinder and ..... that must work - it is starting to - but I am off to bed
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brianeverit
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(Original post by TenOfThem)
The question does not make sense

If the hole has length 4 and goes all the way through then the radius of the sphere would have to be 2
Not at all. If the sphere has radius R and the hole has radius r then the length of the hole will be
2\sqrt(R^2-r^2)
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TenOfThem
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(Original post by brianeverit)
Not at all. If the sphere has radius R and the hole has radius r then the length of the hole will be
2\sqrt(R^2-r^2)
did you see my second post
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brianeverit
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(Original post by TenOfThem)
did you see my second post
Not at the time I quoted you.
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shelaghglenister
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Problem solved once I realised that length of cylinder was not the same as the length of its central core. Thanks
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