(1)A rectangular tank with no top and a volume of 8m3 is to be made from a sheet of metal. The width of the base is 4m. Show that the surface area is given by

S = 4x + 4 + 16/x , wherexis the length of the base and find the dimensions of the tank so that minimum material is used.

(2) The breaking weight of a cantilever beam is directly proportional to b*d^2, wherebis the breadth of the beam anddis its depth. Find the cross-section dimensions of a beam with a cross-section perimeter of 60cm that has maximum breaking weight.

(3)An oil tank, designed to hold 10 m3, is in the form of a cylinder with hemispherical top.

(i) Show that the surface area (A) of the tank is given by A = 20/r + 5/3 * πr^2 , whereris the radius andhis height of the cylinder.

(ii) Find the dimensions (randh) of the tank that has least surface area and calculate the least surface area.