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

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 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 ?

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

A non-viscous liquid of constant density 1000kg//m^3 flows in a streamline motion along a tube of variable cross section. The tube is kept inclined in the vertical plane as shown in Figure. The area of cross section of the tube two point P and Q at heights of 2 metres and 5 metres are respectively 4xx10^-3m^2 and 8xx10^-3m^2 . The velocity of the liquid at point P is 1m//s . Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q.

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 container, open from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre. also find the cost of metal sheet used to make the container, if it cost Rs 8 per 100 cm^(2) (Take pi=3.14)