In this experiment you will measure 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. You are provided with: • a drinks cup with a capacity of approximately 200 cm³ • a 30 cm ruler • a metre rule • approximately 80 cm of thin string • a 250 cm³ measuring cylinder • a supply of water.

1. (a)method 1 Fig. 1.1 shows the measurements to be taken. [Figure 1.1]
2. (a)(i)Measure the height h, the diameter D and the diameter d of the cup provided. h = cm D = cm d = cm[2]
3. (a)(ii)Calculate the average diameter d_A of the cup using your readings from (a)(i) and the equation: d_A = (D + d) / 2 d_A = cm[1]
4. (a)(iii)Calculate a value for the capacity V_1 of the cup using the equation: V_1 = π d_A² h / 4 V_1 = cm³[1]
5. (b)method 2 Use the string and the metre rule to determine the average circumference C of the cup.
6. (b)(i)Describe the method you use and show your working. You may draw a diagram, if you wish. C = cm[2]
7. (b)(ii)Calculate a value for the capacity V_2 of the cup using the equation: V_2 = C²h / (4π) V_2 = cm³[1]
8. (c)method 3 Pour water into the measuring cylinder up to a level that is greater than 200 cm³ and record the volume. This is reading R_1. Pour water from the measuring cylinder into the cup until it is full and record the volume of water left in the measuring cylinder. This is reading R_2. Determine the volume of water V_3 in the cup. Show your working. R_1 = cm³ R_2 = cm³ V_3 = cm³[1]
9. (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]

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