Question 5 - 20 marks This question is based on your work on MU123 up to and including Unit 8. (a) Figure 2 shows a cuboid and a solid cylinder (not drawn to scale). Edge BC has length 6.5 cm, and the diagonal AC has length 14 cm. The radius r of the cylinder is 3.5 em, and the height h is 9cm. r =3.5 cm E A h = 9 cm 14 cm 6.5 cmi C Figure 2 Give your answers to each of the following to two significant figures. (i) Find the surface area of the cylinder. [2] (ii) Find the volume of the cylinder. [2] (iii) Use Pythagoras' Theorem in triangle ABC to find the length of side AB. (2] (iv) If the volume of the cylinder is equal to the volume of the cuboid, find the depth AD of the cuboid, showing your working at each stage. [4](b) In this part of the question, you are asked to comment on a student's attempt at answering the question detailed below. State whether you agree or disagree with what the student has written for each answer, explaining your reasoning in either case. [4] The question For each of the two pairs of triangles shown in Figure 3, determine (if possible) whether the triangles are congruent, explaining your answers. (1) (2) Figure 3 The student's attempt For pair (1), each triangle has sides of lengths 16cm, 20cm and 24 cm so the two triangles are congruent by sss. For pair (2), each triangle has the same three angles and each triangle has a side of length 18 cm. There fore the triangles are congruent by ASA.(c) In Figure 4, BD is a straight line. The straight lines AB and FD are parallel. The straight lines FB and EC are parallel. ZABF = 46 and ZDCE = 880. C E Figure 4 (i) Find Zo, explaining your reasoning. (ii) Find 28, explaining your reasoning. (iii) Find Zy, explaining your reasoning- (iv) What does your answer to part (c)(iii) tell you about triangle FBD? Explain your reasoning. [2]