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.

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.

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 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 a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Also, find the maximum volume.

If A(x, y), B (1, 2) and C (2, 1) are the vertices of a triangle of area 6 square units, show that x+y=15 or -9 .

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?

An open tank is to be constructed with square base and vertical sides so as to contain a given quantity of water. Show that the expenses of lining with lead will be least, if depth is made half of width.

An open tank is to be constructed with square base and vertical sides so as to contain a given quantity of water. Show that the expenses of lining with lead will be least, if depth is made half of width.

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 ?