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# Theoretical Deduction : Cylinder & Sphere

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RC Moderator
Joined: 24 Aug 2016
Posts: 790
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
Theoretical Deduction : Cylinder & Sphere  [#permalink]

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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.
Manager
Joined: 17 May 2015
Posts: 247
Re: Theoretical Deduction : Cylinder & Sphere  [#permalink]

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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 [ 10.84 KiB | Viewed 490 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
Joined: 24 Aug 2016
Posts: 790
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
Re: Theoretical Deduction : Cylinder & Sphere  [#permalink]

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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.
Re: Theoretical Deduction : Cylinder & Sphere   [#permalink] 19 Mar 2018, 05:06
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# Theoretical Deduction : Cylinder & Sphere

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