5. A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter , find the length of the wire.
The figure for the problem is shown below :
Using geometry we can write :
Thus the volume of the frustum is given by :
Now, the radius of the wire is :
Thus the volume of wire is given by :
Now equating volume of frustum and wire, we get :
Thus the length of wire drawn is 7964.44 m.