Assume the slant height of the cone is \(l\) cm. \[ \therefore \pi \times 7 \times l = 154\sqrt{2} \] Or, \[ \frac{22}{\cancel{7}} \times \cancel{7} \times l = 154\sqrt{2} \Rightarrow l = \frac{\cancel{154}7\sqrt{2}}{\cancel{22}} = 7\sqrt{2} \] From the right-angled triangle COB, CB = \(7\sqrt{2}\) cm, OB = 7 cm \[ \therefore \sin \angle OCB = \frac{OB}{CB} = \frac{7}{7\sqrt{2}} = \frac{1}{\sqrt{2}} = \sin 45^\circ \Rightarrow \angle OCB = 45^\circ \Rightarrow \angle ACB = 2 \times \angle OCB = 2 \times 45^\circ = 90^\circ \] \[ \therefore \text{Apex angle of the right circular cone is } 90^\circ \]