Show that the height of the cylinder, op...

Show that the height of the cylinder, open at the top of given surface area and greatest volume is equal to the radius of its base.

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
MODERN PUBLICATION|Exercise EXERCISE|433 Videos
APPLICATIONS OF THE INTEGRALS
MODERN PUBLICATION|Exercise EXERCISE|211 Videos

Similar Questions

Explore conceptually related problems

Show that a cylinder of given volume, open at the top, has minimum total surface area if its height is equal to radius of the base.

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.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 time the radius of the base.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 times the radius of the base.

Show that the height of a closed right-circular cylinder of given volume and least surface area is equal to its diameter.

If the height of a cylinder is doubled and radius remains the same, then volume will be

Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm^2 .

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm is 20/sqrt3 cm. Also find the maximum volume of the cylinder.

MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE

A window is in the form of a rectangle surmounted by a semi-circular o...
Text Solution
|
A window consists if a semi-circle with a rectangel on its diameter. I...
Text Solution
|
Show that the height of the cylinder, open at the top of given surface...
Text Solution
|
Show that the height of the cylinder, open at the top of given surface...
Text Solution
|
Show that the height of a closed right-circular cylinder of given volu...
Text Solution
|
Given the sum of the perimiter of a square and a circle, show that the...
Text Solution
|
A square piece of tin of side 24 cm is to be made into a box without t...
Text Solution
|
A square-based tank of capacity 250 cu m has to bedug out. The cost of...
Text Solution
|
A tank with rectangular base and rectangular sides, open at the top is...
Text Solution
|
A rectangular sheet of tin 45 cm x 24 cm is to be made into a box with...
Text Solution
|
An open box with a square base is to be made out of a given iron sheet...
Text Solution
|
A farmer wants to construct a circular well and a square garden in his...
Text Solution
|
An open tank with a square base and vertical sides is to be constructe...
Text Solution
|
A helicopter is flying along the curve y = x^2+2. A solider is placed ...
Text Solution
|
Find the rate of change of the area of a circle with respect to its ra...
Text Solution
|
The total revenue in Rupees received from its sale of x units of a pro...
Text Solution
|
The interval in which y = x^2 e^-x is increasing is:
Text Solution
|
The slope of the normal to the curve y = 2x^2+3 sinx at x=0 is:
Text Solution
|
The line y = x+1, is a tangent to the curve y^2 = 4x at the point.
Text Solution
|
If f(x) = 3x^2+15x+5, then the approximate value of f (3.02) is :
Text Solution
|