Show that the right circular cylinder of...

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
NCERT BANGLISH|Exercise EXERCISE 6.6|24 Videos
APPLICATION OF DERIVATIVES
NCERT BANGLISH|Exercise EXERCISE 6.4|23 Videos
APPLICATION OF INTEGRALS
NCERT BANGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt(2) time the radius of the base.

Show that the height of a cylinder of given total surface area and open at the top has maximum volumes is equal to the radius of its base .

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is sin^(-1) ((1)/(3)) .

If the volume of a right circular cylinder is 9pih m^3 where h is its height (in metres) then the diameter of the base of the cylinder is equal to___

In a right circular cylinder, if the length of radius is halved and height is doubled, then the volume of cylinder will be

A sphere is inscribed in a right circular cylinder . Prove that the total surface area of the sphere is equal to the curved surface area of the cylinder .

The diameter of the base and height of a solid right circular cylinder are both 21cm. Find the sphere of maximum volume that can be obtained from the cylinder. Find the ratio of the volumes of the cylinder and sphere.

The base radius of a right circular cylinder and a cone are equal and the ratio of their volume is 3:2. Prove that the height of the cone is twice the height of the cylinder.

The radius of base and height of a right circular cone are equal . If the cone be melted to make a right circular cylinder of same radius , then what will be the ratio of the height of cylinder and the slant height of the cone ?

NCERT BANGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.5

Find the maximum value of 2x^(3) – 24x + 107 in the interval [1, 3]. F...
Text Solution
|
It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attai...
Text Solution
|
Find the maximum and minimum values of x + sin 2x on [0, 2pi].
Text Solution
|
Find two numbers whose sum is 24 and whose product is as large as poss...
Text Solution
|
Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...
Text Solution
|
Find two positive numbers x and y such that their sum is 35 and the pr...
Text Solution
|
Find two positive numbers whose sum is 16 and the sum of whose cubes i...
Text Solution
|
A square piece of tin of side 18 cm is to be made into a box without t...
Text Solution
|
A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wit...
Text Solution
|
Show that of all the rectangles inscribed in a given fixed circle, the...
Text Solution
|
Show that the right circular cylinder of given surface and maximum vol...
Text Solution
|
Of all the closed cylindrical cans (right circular), of a given volume...
Text Solution
|
A wire of length 28 m is to be cut into two pieces. One of the pieces ...
Text Solution
|
Prove that the volume of the largest cone that can be inscribed in a s...
Text Solution
|
Show that the right circular cone of least curved surface and given vo...
Text Solution
|
Show that the semi-vertical angle of the cone of the maximum volume an...
Text Solution
|
Show that semi-vertical angle of right circular cone of given surface ...
Text Solution
|
The point on the curve x^(2) = 2y which is nearest to the point (0, 5)...
Text Solution
|
For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2))...
Text Solution
|
The maximum value of [ x(x-1)+1]^((1)/(3)) , 0 lt= x lt= 1 is
Text Solution
|