If an open box with square base is to be made of a given quantitiy of card board of area `c^(2)`, then show that the maximum volume of the box is `c^(3)/(6sqrt(3))` cu units.

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

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

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

A rectangular box with an open top is constructed from cardboard to have a square base of area x^(2) and height h. If the volume of this box is 50 cubic units, how many square units of cardboard in terms of x, are needed to build this box ?

A pyramid with vertex at point P has a regular hexagonal base A B C D E F , Position vector of points A and B are hat i and hat i + 2 hat j The centre of base has the position vector hat i+ hat j+sqrt(3) hat kdot Altitude drawn from P on the base meets the diagonal A D at point Gdot find the all possible position vectors of Gdot It is given that the volume of the pyramid is 6sqrt(3) cubic units and A P is 5 units.

A sheet of area 40m^2 is used to make an open tank with square base. Find the dimensions of the base such that the volume of this tank is maximum.

If the surface area of an open cylinder is 100 cm^(2) , prove that its maximum volume will be 1000/(3sqrt(3pi) cm^(3) .

A 3-inch-tall rectangular box with a square base is constructed to hold a circular pie that has a diameter of 8 inches. Both are shown below. What is the volume, in cubic inches, of the smallest such box that can hold this pie?

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?

A box is constructed by cutting 3-inche square from the corner of a square sheet of cardboard, as shown in the accompanying diagram, and then folding the sides up. If the volume of the box is 75 inches, find the number of square inches in the area of the original sheet of cardboard?