ods rea ca am t Gr 1. A cardboard manufacturing company has been producing milk cartons with the following dimensions. 70 mm 160 mm Find the volume of this container in mm. b) Find the capacity of this container in mL. 190 mm c) How many litres of milk would the container hold? (3 marks) (1 mark) (1 mark) ge 8 19 Libe MP d) Not including the top tab, how much cardboard is required to make this carton? 2. (3 marks) The company was concerned that the carton did not use the materials efficiently, and was considering another carton in the shape of a rectangular prism. If it was to hold the same amount of milk as their other carton, had a square base and was 18 cm high. a) Let x be the length of the sides of the square base. Find the (1 mark) area of the square base in terms of x. b) Hence, find the value of x, the length of the square base. 3. The manufacturer wants to try a cylindrical carton this time that can contain the same amount of milk. For aesthetic purposes, the height of the cylinder will be four times its radius. (2 marks) a) Find the rule for the volume of this cylinder in terms of its radius. (2 marks) b) Hence, show that the radius of this cylinder is equal to 4.086 (2 marks) cm correct to 3 decimal places. c) Find the total amount of cardboard needed to make the cylindrical carton. d) Which of the above cartons would be more productive for the company (which container will cost less)? Explain. (2 marks) (3 marks)