The volume of the greatest cylinder which can be inscribed in a cone of height 30 cm and semi-vertical angle `30^0` is (a)`4000pi/(sqrt(3))` (b) `4000pi/3c m^3` (c) `4000pi/(sqrt(3)c m^3` (d) none of these

Find the maximum volume of the cylinder which can be inscribed in a sphere of radius 3sqrt(3)cm (Leave the answer in terms of pi )

Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius 5sqrt(3)c m is 500pic m^3dot

sin^-1 (cos(sin^-1(sqrt(3)/2))= (A) pi/3 (B) pi/6 (C) - pi/6 (D) none of these

sin^-1 (-1/2)+tan^-1 (sqrt(3))= (A) -pi/6 (B) pi/3 (C) pi/6 (D) none of these

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 4/(27)pih^3tan^2alphadot

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is (a) 4/3pi (b) (10)/3pi (c) 5pi (d) (20)/3pi

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (4pi)/3 (d) (5pi)/3 (e) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

In Fig. 15.109, the area of segment A C B is (FIGURE) (a) (pi/3-(sqrt(3))/2)\ r^2 (b) (pi/3+(sqrt(3))/2)\ r^2 (c) (pi/3-2/(sqrt(3)))\ r^2 (d) None of these

The area of the circle that can be inscribed in a square of side 10 cm is (a) 40pi\ c m^2 (b) 30pi\ c m^2 (c) 100\ pi\ c m^2 (d) 25\ pi\ c m^2