Show that the height of the cylinder ...

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height `h` is `1/3h`

Text Solution

Verified by Experts

The correct Answer is:

`(h)/(3)`

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
MODERN PUBLICATION|Exercise Questions From NCERT Exemplar|7 Videos
APPLICATIONS OF DERIVATIVES
MODERN PUBLICATION|Exercise EXERCISE 6 (a) (Short Answer Type Questions)|15 Videos
APPLICATIONS OF DERIVATIVES
MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos
APPLICATIONS OF THE INTEGRALS
MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is (1)/(3)h

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 2(R)/(sqrt(3)) .Also find maximum volume.

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

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

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

The height of the cylinder of maximum volume which can be inscribed in a sphere of radius 3cm is

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle? is one-third that of the cone and the greatest volume of cylinder is (4)/(27)pi h^(3)tan^(2)alpha

The height of the cylinder of the greatest volume that can be inscribed in a sphere of radius 3 is

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-Frequently Asked Questions

Find two positive number whose sum is 24 and their sum of square is mi...
Text Solution
|
Show that all the rectangles with a given perimeter, the square has...
Text Solution
|
Show that the rectangle of maximum perimeter which can be inscribed...
Text Solution
|
Show that the triangle of maximum area that can be inscribed in a g...
Text Solution
|
An open box with a square base is to be made out of a given iron sheet...
Text Solution
|
40. A given quantity of metal is to be cast into a half cylinder with ...
Text Solution
|
A window has the shape of a rectangle surmounted by an equilateral ...
Text Solution
|
Show that the height of the cylinder of maximum volume that can be ...
Text Solution
|
Let AP and BQ be two vertical poles at points A and B, respectively. ...
Text Solution
|
If length of three sides of a trapezium other than base are equal t...
Text Solution
|
A square piece of tin of side 24 cm is to be made into a box without t...
Text Solution
|
A metal box with a square base and vertical sides is to contain 102...
Text Solution
|
A tank with rectangular base and rectangular sides, open at the top...
Text Solution
|
Show that the right circular cylinder, open at the top, and of give...
Text Solution
|
Find the point on the curve y^2=4x which is nearest to the point (2, 1...
Text Solution
|
An Apache helicopter of enemy is flying along the curve given by y=x^...
Text Solution
|
An open tank with a square base and vertical sides is to be constru...
Text Solution
|
A cuboidal shaped godown with square base is to be constructed. Three ...
Text Solution
|
A manufacturer can sell x items at a price of Rs. (5-x/(100)) each. Th...
Text Solution
|
A person wants to plant some trees in his community park. The local nu...
Text Solution
|