Show that semi-vertical angle of right circular cone of given surface area and maximum volume is `sin^-1(1/3)`.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 times the radius of the base.

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

Calculate the surface area and volume of a sphere of radius '3 cm .'

If theta is semi vertical angle of a cone of maximum volume and given slant height, then tantheta is equal to

Show that all rectangles with a given perimeter, the square has the maximum area.

Radius and slant height of a solid right circular cone are 35cm and 37cm respectively,Find the curved surface area and total surface area of the cone.

An open box with a square base is to be made out of a given quantity of sheet of area a^2 . Show that the maximum volume is (a^3)/(6sqrt3) .