Home
Class 12
MATHS
The height of a right circular cylinder ...

The height of a right circular cylinder of maxium volume inscribed in a sphere of radius 3 cm is

A

A. ` sqrt6 `

B

B. `sqrt 3 `

C

C. ` ( 2 ) / (3 ) sqrt 3 `

D

D. `2 sqrt 3 `

Text Solution

Verified by Experts


` h = 2 (3 cos theta ) `
` r = 3 sin theta , v = pi r ^ 2 h , = pi 9 sin ^ 2 theta . 6 cos theta `
` V = 54 pi sin 2 theta cos theta , (dv ) / ( d theta ) = 0 `
` rArr 2 sin theta cos ^ 2 theta - sin ^ 3 theta = 0 rArr 2s ( 1 - s ^ 2 ) - s ^ 3 = 0 rArr 2 s - 2s ^ 3 - s ^ 3 = 0 `
` rArr 2 s - 3s ^ 3 = 0 rArr s = 0 or 2 - 3s ^ 2 = 0 `
` s = pm sqrt ((2 ) /(3)) therefore cos theta = sqrt( 1 - ( 2 ) /(3 ) ) = (1 ) /(sqrt 3 ) `
` h = 6 ((1 )/(sqrt3 )), h = 2 sqrt 3 `
Promotional Banner

Topper's Solved these Questions

  • JEE Main Revision Test-9 | JEE-2020

    VMC MODULES ENGLISH|Exercise SECTION 2|5 Videos

  • JEE Main Revision Test-6 | JEE-2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

Show that the height of the right circular cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3))

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) .

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) .

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) .

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius R is (4R)/3dot

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4R)/3dot Also find maximum volume in terms of volume of the sphere.

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also, find maximum volume in terms of volume of the sphere.

Show that the height of the right circular cylinder of maximum volume that can be inscribed in a given right circular cone of height h is (h)/(3)

If a right circular cylinder of height 10 is inscribed in a sphere of radius 6, what is the volume of the cylinder ?