Question 5 - 20 marks Throughout this question, take care to explain your reasoning carefully. You should round your answers, where necessary, to two significant figures. In this question you may assume that the Earth is spherical, with diameter 12 700 km. A telecommunications company owns satellites A, B, C and D, which are in orbit around the Earth. At a particular instant in time all the satellites lie on a circle whose diameter crosses the centre of the Earth and which is 250 km above the surface of the Earth. Satellite A is diametrically opposite satellite B (i.e. AB is a diameter of the orbit and passes through the centre of the Earth). Satellite C is 5100 km from satellite A. ZACB is 909, ZACD is 150, and ZDAC is 14. (a) (i) Draw a diagram of the Earth and the satellites, shown as points, including all the information given in the question. Your diagram does not need to be to scale. [2] (ii) Find the surface area of the sphere which the satellites lie on at this moment in time. [2] (iii) Find the length BC. [2] (iv) Calculate ZBAC. (v) Is triangle ABC similar to triangle ACD? Explain your answer. (vi) Calculate the length CD. (vii) Find the area of triangle ACD. [3] (b) You may assume that the Moon is spherical with radius 1700 km. A scale model of the Earth and the Moon is made. In the model, the radius of the Moon is 85 cm. (i) Find the radius of the scale model of the Earth. [2] (ii) Find the volume of the scale model of the Earth. [2]