An open cylindrical tank whose base is a circle is to be constructed
of metal sheet so as to contain a volume of `pi``a^3` cu. cm of water.
Find the dimensions so that sheet required is minimum.

As shown in the figure, a cylindrical glass contains water. A metal shpere of diameter 2 cm is immersed in the water. Find the volume of water.

Find the area of the sheet required to make a cylindrical container. Which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

An open box with a square base is to be made out of a given quantity of sheet of area a^2 , Show the maximum volume of the box is frac {a^3}{6 sqrt 3}

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of right circular cone mounted on a hemisphere is immersed into the tub. The radius of the hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm. Find the volume of water left in the tub. ("Take "pi=22/7)

Find the height of a covered box of fixed volume so that the total surface area of the box is minimum whose base is a rectangle with one side three times as long as the other.