Question 2 11] marks You should be abte to answer this question aer studying Unit 7. Tanya wants to make an aluminium open-topped water tank to collect rain water in her garden. She wants the total capacity of the water tank to be 32 m3. The water tank is a square-based cuboid with its top face removed. It comprises ve faces; a square base of length and width mm, and four vertical wall pieces of height hm. Tanya wants to minimise the total area of aluminium required to build the water tank. {a} {b} {C} hm Write down an equation for the total volume of the tank in terms of the height h and width in. Use this equation to express h in terms of w. [2] Show that the total surface area A, in terms of w, is 128 A = w2 + . [3] w Use dierentiation to determine the width is that gives the minimum surface area A of the water tank, and show that this is a minimum. What is the minimum surface area of the water tank? [5]