Throughout this question, take care to erplain your reasoning carefully. You should round your answers, where necessary, to two significant figures. A student is making a model crane for an investigation. She makes two component models. Model 1 is of the caterpillar track base (how it's going to move), and Model 2 is of the hydraulic arm. (a) A cross-section view of one of the two caterpillar tracks used in the model is given in Figure 2. It is comprised of 2 wheels, each of radius 3 cm. The distance between the centres of the wheels is 20 cm. The caterpillar track is represented as a solid line in Figure 2, that is the straight line from A to B, the outer semicircle from B to C, the straight line from C to D and outer semicircle from D to A. 20 cm Figure 2 (i} Find the total length of a caterpillar track (the solid line). [2] (ii) Find the area of the circular face of one of the wheels. [2] A diagram of Model 2, the hydraulic arm, is given in Figure 3 and shows a base AB of length 10 cm and a vertical post BG. The angle AB(G 15 a right angle. The vertical post is braced by a bar of length 17 em, represented by the line AC. A bar represented by the line F'(Z can be raised or lowered by increasing or decreasing the length of a vertical hydraulic ram represented by the line ED). In its present position, ED is set at 20cm so that F(7 and AC are parallel. The length of FE is 26 cm. G 26 cm 20 cm C D F 17 cm A 10 cm B Figure 3 (i) Use Pythagoras' Theorem to calculate the length BC (ignoring the thickness of the material). ii) Calculate ZACB. (iii) Find the angles ZFGB and ZFED. Explain your answer. [2] (iv) Calculate the length FD. (v) Given that ZEFD is acute, use your answers to parts (b) (iii) and (iv) to calculate ZEFD [3] (vi) In a planned full-size version of the hydraulic arm, the bar AC has length 2.55 m. Find the length corresponding to FE in the full-size version in metres. [2]