Question 2 - 8 marks You should be able to answer this question after studying Unit 1. Consider the following TMA question and two possible student solutions. Both solutions contain some errors in the calculation, which result in a wrong solution. Question An artist is making an exhibition piece comprising of a cylinder and a cube, where they wish the cube to have the same surface area as the cylinder. The cylinder has already been made and has a diameter of 30 cm and a height of 45 cm. How long should the side of the cube be to have the same surface area as the cylinder? Give your answer to one decimal place. Poorly-written solution Cylinder = 2r2 + 2rh = 4335 = Cube side length = 26.9 Well-written solution 1 Surface area of a cylinder with radius r and height h in cm Surface area = 2r2 + 2rh = 2 15 + 2 15 45 = 4335.397 . . . cm2 Surface area of a cube of side s cm Surface area = 6 s 2 This area must be the same as above for the cylinder, so 6s 2 = 4335.397 . . . s 2 = 722.566 . . . s = 722.566 . . . = 26.880 . . . . Choosing the positive square root because lengths cannot be negative, the cube will have a side length of 26.9 cm (to one decimal place). (a) Without commenting on the calculation errors, suggest three ways in which the well-written solution is better than the poorly written solution (and so is likely to be awarded considerably higher marks).