69 3 H As it is shown in the diagram, the proportion of the height of the container that is filled is =. The current volume of water is 90 × 40 × 80 = 288 000 cm3. Assume you move the container so that the base is 40 × 120. The volume of M1 M1 for method of finding proportion of height water must stay the same and take its height as cm. Then: A1 for C A1 B1 for 288 000 40 × 120 × = 288 000 C B1 so 4800 × = 288 000 C = 60 C C1 for clear explanation of changing to a different base Comparing this with the height, 90 cm: C2 C1 for structure and clarity of explanation = Now assume you move the container so the base is 90 × 120 then 90 × 120 × = 288 000 C 10 800C = 288 000 = C Comparing this with the height, 40 cm: = = = C1 for clear explanation of changing to a different base So the proportion of the height of the C2 C1 for structure and clarity of explanation container that is filled with water remains constant. C1 for clear explanation C1 8 A1 for clear complete explanation of solution
69 As it is shown in the diagram, the proportion of the height of the container that is filled is =. The current volume of water is 90 × 40 × 80 = 288 000 cm3. Assume you move the container so that the base is 40 × 120. The volume of water must stay the same and take its height as C cm. Then: 40 × 120 × C = 288 000 so 4800 × C = 288 000 C = 60 Comparing this with the height, 90 cm: = Now assume you move the container so the base is 90 × 120 then 90 × 120 × C = 288 000 10 800C = 288 000 C = Comparing this with the height, 40 cm: = = = So the proportion of the height of the container that is filled with water remains constant. M1 A1 B1 C2 C2 C1 3 M1 for method of finding proportion of height A1 for B1 for 288 000 C1 for clear explanation of changing to a different base C1 for structure and clarity of explanation C1 for clear explanation of changing to a different base C1 for structure and clarity of explanation C1 for clear explanation A1 for clear complete explanation of solution H 8