QUESTION 1 (a) A regular icosahedron of side length x cm, shown in the Figure 1, is expanding uniformly. The icosahedron consists of 20 congruent equilateral triangular faces of side length x cm. Figure 1 Show that the surface area, A cm, of the icosahedron is given by A = 5v3x2 . (2) Given that the volume, Icm, of the icosahedron is given by V = - 12 (3+15) x3. 11 . Show that dV (3 + v5)x dA (3) 8V3 The surface area of the icosahedron is increasing at a constant rate of 0.025 cm-s-1. Find the rate of change of the volume of the icosahedron when x = 2, giving your answer to 2 significant figures. (3) 0.8 (b) Use trapezium rule with four strips, to evaluate (e- +1) dx (4)