Question

A cone is inscribed in a cube so that the base of the cone is inscribed in one of the faces of the cube and the vertex of the cone is the cone is the centre of the opposite face; find the ratio of the volumes of the cube and cone.

Answer 1

volume of cube=  A³  (A is the side of a cube)
volume of cone =1/3(πr²h)   (r=radius, h=height)
    but, r=A/2 and h=A putting values
volume of cone= 1/3[π(A/2)²A]
                       =1/3[(πA³)/4]
                      =(πA³)/12
ratio = A³/πA³/12
       =A³×12/πA³          
      =12/π
     =12/22/7
     =12×7/22
    =84/22
  =42/11