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Differential Calculus

Blazing goIITian

Joined:	15 Jul 2008
Post:	315

16 Aug 2009 03:07:59 IST

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Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R

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Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is. Also find the maximum volume.

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kabi

Blazing goIITian

Joined: 11 Jan 2009

Posts: 575

17 Aug 2009 21:40:14 IST

Like 1 people liked this

See the pics below

Height = 2 R sin (theta )

Volume = pi (Rcos(theta))² ( 2 R sin( theta ))

Let A = cos ²(theta ) sin (theta)

dA/ d (theta ) = 0

cos(theta ) [ ( cos² (theta ) - 2 sin²(theta ) ] = 0

now cos (theta ) can't be zero

so from second equation

tan(theta ) = 1 /sqrt(2)

sin(theta) = 1/ Sqrt(3)

Height = 2 R / Sqrt(3)

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