Q. 17 5.0( 3 Votes )

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

Answer :

Let the radius, height and volume of cylinder be r, h and V respectively

Radius of sphere = R (Given)

Volume of cylinder, V = πr2h …1

OC = R

BC = r

In triangle OBC,

+ r2 = R2

r2 = R2 - …2

Replacing equation 2 in equation 1, we get

V = π (R2 - )(h) = πR2h -

Condition for maxima and minima is

= 0

Since, h cannot be negative


For < 0

V will be maximum for

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Show that the maximum value of is

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The maximum value of is:

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