(a) Length of the arc XY = Circumference of the base. \(\frac{\theta}{360^\circ} \times 2\pi r\) where \(\theta\) = 270^\circ ; r = 7cm. Length of arc XY = \(\frac{270^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 7 = 33cm\) Let the radius of the base of the cone = x \(2 \pi r = 33cm\) \(2 \times \frac{22}{7} \times x = 33\) \(\frac{44}{7} \times x = 33 \implies x = \frac{33 \times 7}{44}\) \(x = 5.25cm\) (b) Area of the base of the cone = \(\pi r^{2}\) = \(\frac{22}{7} \times \frac{21}{4} \times \frac{21}{4}\) = \(\frac{693}{8} cm^{2} = 86.625 cm^{2}\) \(\approxeq 87 cm^{2}\)