An open topped box is to be constructed by removing equal squares from each corner of a `3` metre by `8` metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

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.

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 from the box. What should be the side of the square to be cut off so that the volume of the box is maximum?

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.

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 rectangle sheet of tin with adjascent sides 45 cm and 24 cm is to be made into a box without top, by cutting off equal squares of side x from the corners the folding up the flaps. For what value of x, the volume of the box will be maximum.

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8m^3 . If the building of tank costs Rs. 70//sq metres for the base and Rs. 45//_"square" metres. For sides, what is the cost of least expensive tank?

From the four corners of a rectangle, small squares are cut off and the sides are folded up to make a box, as shown below:(fig) i) Taking a side of the square as x cm, write the dimensions of the boxin terms of x. ii) Taking the volume of the box as v(x) cubic cm, write the relation between v(x) and x as an equation.

In the newly constructed auditorium in the school, there are 8 cylindrical shaped pillars of same size. Each pillar has a height of 4 cm . Dlameter of the pillar is 1 meter. i. Find the curved surface area of a pillar. ii. Find the curved surface area of 8 pillars. iii. If it cost 160 rupees to paint one square metre, how much will it cost?