(b) consider a paper disc whose boundary is the circle in part (a). The sector AOB is removed from the paper disc and the remaining paper is bent round to form a shallow cone by joining the edge OB to the edge OA.

(i) Which arc becomes the circle that is at the base of the cone? Find the angle subtended by this arc in the original circle (in radians), and hence find the length of the arc.

(ii) Hence find the radius of the circle that is at the base of the cone.

(iii) Find the perpendicular height of the cone.

(iv)Given that the formula for the volume of a cone is

V = 1/3 pie r^2 h

(Where r is the radius of the base and h is the perpendicular

Height), find the volume of the cone in this question.