A metal box with a square box and vertical sides is to contain `512 c^3` of volume. The material for the top and bottom costs Rs. `5 cm^2` and that for the sides costs Rs. `2.50 cm^2`. Find the least cost of the box.

The outer Surface of the cube of side 6 m is painted. If the cost of painting is Rs. 1 per 100 " cm"^2 . Find the total cost of painting the cube.

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of the material will be least when the depth of the tank is half of its width.

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5per cm^2 . Find the cost of painting.

The cost of one bicycle is Rs.675.Find the cost of 2 dozen bicycles.

If the cost of fencing a square plot at the rate of Rs. 2.50 per m is Rs. 300. Then find the length of each side of the field.

A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 m3. If building of tank costs Rs. 100 per square metre for the base and Rs. 50 per square metres for the sides, find the cost of least expensive tank.

A path 5 m wide runs along inside a square park of side 100 m. Find the area of the path. Also find the cost of cementing it at the rate of Rs. 250 per 10 m^2