Mathematics Integration Level: Misc Level

Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube

Mathematics Integration Level: Misc Level

An open box with a square base is to be made of given iron sheet of area 27 square meters. Show that the maximum volume of the box is 13.5 cubic meter.

Mathematics Integration Level: Misc Level

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top by cutting off squares from the corners and folding up the flaps. What should be the side of the square in order that the volume of the box is maximum?

Mathematics Integration Level: Misc Level

A closed right circular cylinder has a volume of 2156 cubic cm. What will be the radius of its base so that its total surface area is minimum? Find the height of the cylinder when its total surface is minimum. Take =22/7

Mathematics Integration Level: Misc Level

Find the maximum volume of the cylinder which can be insrcribed in a sphere of radius cm. (Leave the answer in terms of )

Mathematics Integration Level: Misc Level

Show that the semi-vertical angle of the right circular cone of given total surface area and maximum volume is

Mathematics Integration Level: Misc Level

An open box with a square base is to be made out of a given quantity of cardboard whose area is c² square units. Show that the maximum volume of the box is cubic units.