A student measures the capacity of a drinks cup by three different methods. The capacity of a cup is the maximum volume of liquid that it can hold. (a) method 1 The student measures: • the height h of the cup • the diameter D of the top of the cup • the diameter d of the bottom of the cup. Fig. 1.1 shows a full-size diagram of the cup. D h d [Figure 1.1]

1. (a)(i)Measure the height h, the diameter D and the diameter d of the cup in the diagram. h = cm D = cm d = cm [2][2]
2. (a)(ii)Calculate the average diameter dA of the cup using your readings from (a)(i) and the equation: dA = (D + d) 2 dA = cm [1][1]
3. (a)(iii)Calculate a value for the capacity V₁ of the cup using the equation: V₁ = πdA²h 4 V₁ = cm³ [1][1]
4. (b)(i)The student uses a length of string and a metre rule to determine the average circumference C of the cup. The student: • wraps some of the string 5 times around the cup • measures the length I of string used. l = 87.9 cm Calculate the average circumference C of the cup. C = cm [1][1]
5. (b)(ii)Use your values of h from (a)(i) and C from (b)(i) to calculate a value for the capacity V2 of the cup using the equation: V₂ = C²h 4π V2 = cm³ [1][1]
6. (c)(i)The student: • fills a measuring cylinder with water, up to the 220 cm³ mark • pours water from the measuring cylinder into the cup until the cup is full • records the new reading R on the measuring cylinder. Fig. 1.2 shows the new reading R. cm³ 40 water 20 [Figure 1.2] Write down the new reading R. R = cm³ [1][1]
7. (c)(ii)Determine the volume of water V3 in the cup. Show your working. V3 = cm³ [1][1]
8. (d)All three methods of determining the capacity of the drinks cup give values which are approximate. State one reason why the volume calculated in method 2 and one reason why the volume calculated in method 3 are not accurate. method 2 method 3 [2][2]

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