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Theoretical Deduction : Cylinder & Sphere

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Joined: 24 Aug 2016
Posts: 401
Location: Canada
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
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Theoretical Deduction : Cylinder & Sphere  [#permalink]

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New post 18 Mar 2018, 21:07
Hello Seniors :

In the GMAT CLUB math book I found :

For a cylinder of radius r inscribed in a sphere of radius R (R greater than r)

Height of the cylinder is 2(\(\sqrt{{R^2-r^2}}\))

Could not deduct myself.......could any one help
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

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Joined: 17 May 2015
Posts: 239
Re: Theoretical Deduction : Cylinder & Sphere  [#permalink]

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New post 19 Mar 2018, 02:40
1
u1983 wrote:
Hello Seniors :

In the GMAT CLUB math book I found :

For a cylinder of radius r inscribed in a sphere of radius R (R greater than r)

Height of the cylinder is 2(\(\sqrt{{R^2-r^2}}\))

Could not deduct myself.......could any one help


Hi u1983 ,

Please refer the below diagram:

Attachment:
Cylinder_Sphere.png
Cylinder_Sphere.png [ 10.84 KiB | Viewed 363 times ]


In the right angle triangle ABC , by applying Pythagoras theorem we have following:

\(r^2 + (\frac{h}{2})^2 = R^2\)

After simplifying, we get:

\(\Rightarrow h = 2 \sqrt{R^2 - r^2}\)

Hope this helps.

Thanks.
RC Moderator
User avatar
P
Joined: 24 Aug 2016
Posts: 401
Location: Canada
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
GMAT ToolKit User Reviews Badge CAT Tests
Re: Theoretical Deduction : Cylinder & Sphere  [#permalink]

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New post 19 Mar 2018, 05:06
ganand wrote:
u1983 wrote:
Hello Seniors :

In the GMAT CLUB math book I found :

For a cylinder of radius r inscribed in a sphere of radius R (R greater than r)

Height of the cylinder is 2(\(\sqrt{{R^2-r^2}}\))

Could not deduct myself.......could any one help


Hi u1983 ,

Please refer the below diagram:

Attachment:
Cylinder_Sphere.png


In the right angle triangle ABC , by applying Pythagoras theorem we have following:

\(r^2 + (\frac{h}{2})^2 = R^2\)

After simplifying, we get:

\(\Rightarrow h = 2 \sqrt{R^2 - r^2}\)

Hope this helps.

Thanks.



Thanks a bunch......... earlier I was having difficulty to visualize the \(\frac{h}{2}\) portion.
It is clear now.
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

GMAT Club Bot
Re: Theoretical Deduction : Cylinder & Sphere &nbs [#permalink] 19 Mar 2018, 05:06
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Theoretical Deduction : Cylinder & Sphere

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