question_answer 1)

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is of the volume of the sphere.  

Answer:

Let r be the radius and h and the height of the cone.       In fig. OH = h ? R             In  R2 = r2 + (h ? R)2               ?. (1)       Volume of cone                                      (by (1))                                                               ?. (2)                         4Rh = 3h2             4R = 3h             h = 4R/3             Now                                      is maximum when                                                       Hence volume of largest cone  volume of the sphere hence the result.