Show that the height of the cylinder of ...

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.

Text Solution

Verified by Experts

The correct Answer is:

`(4pi R^(3))/(3sqrt(3))`

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
KUMAR PRAKASHAN|Exercise PRACTICE WORK|85 Videos
APPLICATION OF DERIVATIVES
KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos
APPLICATION OF DERIVATIVES
KUMAR PRAKASHAN|Exercise EXERCISE - 6.5|47 Videos
ANNUAL EXAMINATION :SAMPLE PAPER
KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos
APPLICATION OF INTEGRALS
KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

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) .

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere.

Show that a triangle of maximum area that can be inscribed in a circle of radius a is an equilateral triangle.

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 alpha is one - third that of the cone and the greatest volume of cylinder is (4pi)/(27)h^(3) tan^(2)alpha .

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1)sqrt(2) .

Find the volume and surface area of a sphere of radius 2.1 cm (pi = (22)/(7))

Find the volume of a sphere of radius 11.2 cm.

Find the volume of sphere of radius 6.3 cm

The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius r is given by

Fill in the blanks so as to make each of the following statements true : The area of the largest triangle that can be inscribed in a semicircle of radius r cm is …………. cm^(2) .

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -MISCELANEOUS EXERCISE - 6

Find the intervals in which the function f given f(x)=x^(3)+(1)/(x^(3)...
Text Solution
|
Find the maximum area of an isosceles triangle inscribed in the ellips...
Text Solution
|
A tank with rectangular base and rectangular sides, open at the top is...
Text Solution
|
The sum of the perimeter of a circle and square is k, where k is some ...
Text Solution
|
A window is in the form of a rectangle surmounted by a semicircular op...
Text Solution
|
A point on the hypotenuse of a triangle is at distance a and b from th...
Text Solution
|
Find the points at which the function f given by f(x)=(x-2)^(4)(x+1)^(...
Text Solution
|
Find the points at which the function f given by f(x)=(x-2)^(4)(x+1)^(...
Text Solution
|
Find the points at which the function f given by f(x)=(x-2)^(4)(x+1)^(...
Text Solution
|
Find the absolute maximum and minimum values of the function given by ...
Text Solution
|
Show that the altitude of the right circular cone of maximum volume th...
Text Solution
|
Let f be a function defined on [a,b] such that f'(x)gt 0, for all x in...
Text Solution
|
Show that the height of the cylinder of maximum volume that can be ins...
Text Solution
|
Show that height of the cylinder of greatest volume which can be inscr...
Text Solution
|
A cylindrical tank of radius 10 m is being filled with wheat at the ra...
Text Solution
|
The slope of the tangent to the curve x=t^(2)+3t-8, y=2t^(2)-2t-5 at t...
Text Solution
|
The line y= m x +1 is a tangent to the curve y^2 =4 x if th...
Text Solution
|
The normal at the point (1, 1) on the curve 2y+x^(2)=3 is …………
Text Solution
|
The normal to x^(2)=4y passing through (1, 2) has equation ……….
Text Solution
|
The points on the curve 9y^(2)=x^(3), where the normal to the curve ma...
Text Solution
|