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() y - L 3+3 +3 +3 +3 = 15 marks] 5. Two flies are sitting on a spherical balloon while it is being inflated at a constant rate. Assume that air is being injected into the balloon at a rate of 3 cubic centimetres per second (cm /s), and that the balloon has no air in it to begin with. Further assume that one fly is situated at the north pole and the other on the equator. (a) Draw a picture showing an instant of the balloon with the two flies on it, complete with labels, including the radius r of the balloon. Denote the distance on the balloon between the two flies as s. (b) Noting that the distance s is 1/4 of the circumference of a circle 27r, how fast are the two flies parting company as a function of the radius r? (Hint: Using the formula V = =mrs for the volume of a sphere, find an expression for the rate of change of 3 radius of the balloon as it is inflated. Hence find the rate at which the distance s between the two flies is increasing.) (c) How fast are the two flies parting company when r = 10 cm? (d) How fast when r = 1 cm? (e) How fast when r = 0.1 cm? (f) How fast are they separating initially (when r = 0)? (Hint: Use a limit.)