(a) (i) Length of sector = \(\frac{\theta}{360} \times 2\pi R\) Length of the base of the cone formed = \(2\pi r\) \(\frac{90}{360} \times 2 \times \pi \times 8 = 2\pi r\) \(4\pi = 2\pi r\) \(2r = 4 \implies r = 2 cm\) The base radius of the cone = 2 cm. (ii) Height of the cone \(h^{2} = 8^{2} - 2^{2}\) \(h^{2} = 64 - 4 = 60\) \(h = \sqrt{60}\) = \(7.746 cm\) (iii) volume of a cone = \(\frac{1}{3} \pi r^{2} l\) = \(\frac{1}{3} \times \frac{22}{7} \times 2 \times 2 \times 7.746\) = \(\frac{88 \times 7.746}{21}\) = \(32.46 cm^{3}\) (b)(i) \(100,000 cm = 1 km\) 1 cm represents 20,000 metres \(\therefore 4.5 cm = (4.5 \times 20,000) cm\) = 90,000 cm Converting to km, = \(\frac{90,000}{100,000}\) = 0.9km (ii) 1 metre represents 20,000 metres 16km = 16000m Distance on the map in metres = \(\frac{16000}{20000}\) = 0.8m (iii) Area of the forest on the map = \(\frac{85 \times (10^{5})^{2} cm^{2}}{(20000)^{2}}\) = \(\frac{85 \times 10^{10}}{4 \times 10^{8}}\) = \(2125 cm^{2}\)