Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is `(2R)/(sqrt(3))`. Also find the maximum volume.

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3) .

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere.

Show that a triangle of maximum area that can be inscribed in a circle of radius a is an equilateral triangle.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle alpha is one - third that of the cone and the greatest volume of cylinder is (4pi)/(27)h^(3) tan^(2)alpha .

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1)sqrt(2) .

Find the volume and surface area of a sphere of radius 2.1 cm (pi = (22)/(7))

Find the volume of a sphere of radius 11.2 cm.

Find the volume of sphere of radius 6.3 cm

The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius r is given by

Fill in the blanks so as to make each of the following statements true : The area of the largest triangle that can be inscribed in a semicircle of radius r cm is …………. cm^(2) .