(a) In the diagram above, \(\alpha = 28^\circ\) (angles in alternate segment) \(46^\circ + \beta + \alpha = 180^\circ\) (angles on a straight line) \(46^\circ + \beta + 28^\circ = 74^\circ + \beta = 180^\circ\) \(\beta = 180^\circ - 74^\circ = 106^\circ\) \(x + \beta = 180^\circ\) (opposite angles of a cyclic quadrilateral) \(x + 106^\circ = 180^\circ\) \(x = 180^\circ - 106^\circ = 74^\circ\) Hence, < VUS = 74^\circ. (b) Total surface area = curved surface area + area of closed end = \(2\pi rh + \pi r^{2}\) = \(\pi r(2h + r)\) \(462 = \frac{22r}{7}((2 \times 7) + r)\) \(\frac{462 \times 7}{22} = r(14 + r)\) \(147 = 14r + r^{2}\) \(r^{2} + 14r - 147 = 0\) \(r^{2} - 7r + 21r - 147 = 0\) \(r(r - 7) + 21(r - 7) = 0\) \((r + 21)(r - 7) = 0\) \(r = \text{-21 or 7}\) The radius cannot be negative, therefore, r = 7 cm.