An open box with a square base is to be made out of a given quantity of sheet of area `a^2`.
If the box has side x units, then show that volume `V=(a^2x-x^3)/4`

An open box with a square base is to be made out of a given quantity of sheet of area a^2 . Show that the maximum volume is (a^3)/(6sqrt3) .

If (x+iy)^3 = u + iv , then show that u/x+v/y=4(x^2-y^2)

An open box of maximum value is to be made from a square piece of tin sheet 24 cm on a side by cutting equal squares from the corners and turning of the sides. Complete the following table.

An open box of maximum volume is to be made from a square piece of tin sheet 24 cm on a side by cutting equal squares from the corners and turning of the sides. Using the table, express V as a function of x and determine its domain.

A cuboid with a square base and given volume v is shown in figure: Express surface area 'S' as a function of x.

show that 3x+1=3/4(4x-2)+5/2

A cuboid with a square base and given volume V is shown in figure: Show that the surface area is minimum when it is a cube .

An open box is made by removing squares of equal size from the corners of a tin sheet of size 16cmxx10cm and folding up the sides of the box so obtained. What is the value of x for which V is maximum?

An open box is made by removing squares of equal size from the corners of a tin sheet of size 16cmxx10cm and folding up the sides of the box so obtained. With the help of figure, obtain the relation V=x(16-2x)(10-2x).

A rectangle sheet of tin with adjacent sides 45 cm and 24 cm is to be made into a box without top, by cutting off equal squares from the corners the folding up the flaps. Taking the side of the square cut off as x, express the volume of the box as the function of x.