# 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.

Let 'x' be the diameter of the bare of the cylinder and Let 'h' be height of the cylinder.

In

The volume of cylinder,

On differentiating equation (ii) w.r.t h we get,

Again differentiating equation (iii) w.r.t. h we get,

So, V is maximum when

hence, the highest of the cylinder of maximum volume that can be inscribed in a sphere of radius R is

Hence proved

From (i) , we have

## Related Chapters

### Preparation Products

##### Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
##### Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
##### Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-