Home
Class 12
MATHS
An open box with square base is to be ma...

An open box with square base is to be made of a given quantity of card board of area `c^(2)`. Show that the maximum volume of the box is `(c^(3))/(6sqrt(3))` cubic units.

Text Solution

Verified by Experts

The correct Answer is:
`= (c^(3))/(6sqrt(3))("unit")^(3)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (OBJECTIVE TYPE TYPE QUESTIONS)|25 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (FILLERS)|5 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)|24 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 semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1)sqrt(2) .

A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is (1)/(6) pi a^(3) .

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

A metal box with a square base and vertical sides is to contain 1024 cm^(3) . The materical for the top and bottom costs Rs. 5//cm^(2) and the material for the sides costs Rs. 2.50//cm^(2) . Find the least cost of the box.

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?

If vec(a) is a unit vector and vec(b)=(2,1,-1) and vec( c )=(1,0,3) . Then the maximum value of [vec(a)vec(b)vec( c )] is…………..

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

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.

If the container filled with liquid gets accelerated horizontally or vertically, pressure in liquid gets changed. In liquid ( a_(y) ) for calculation of pressure, effective g is used. A closed box horizontal base 6 m by 6 m and a height 2m is half filled with liquid. It is given a constant horizontal acceleration g//2 and vertical downward acceleration g//2 . The maximum value of water pressure in the box is equal to

Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixed points on the parabola. Let C be a moving point on the parabola between Aa n dB such that the area of the triangle A B C is maximum. Then the coordinates of C are (1/4,1) (b) (4,4) (3,2/(sqrt(3))) (d) (3,-2sqrt(3))