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. (i) Measure the height $h$, the diameter $D$ and the diameter $d$ of the cup in the diagram. $h$ = \_\_\_\_\_\_ $\text{cm}$ $D$ =…

Physics 5054/42 — May/June 2023

Cambridge O-Level · Alternative to Practical · worked solutions for every part, with the mark scheme

questions

marks

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Topics Observations and Measurements · Analysis, Conclusions and Evaluation · Experimental Contexts · Use of Techniques, Apparatus and Materials · Planning Experiments and Investigations

Q110MObservations and MeasurementsAnalysis, Conclusions and EvaluationFree sample

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.

Fig. 1.1

(i)

Measure the height $h$ , the diameter $D$ and the diameter $d$ of the cup in the diagram.

$h$ = ______ $\text{cm}$
$D$ = ______ $\text{cm}$
$d$ = ______ $\text{cm}$

(ii)

Calculate the average diameter $d_A$ of the cup using your readings from (a)(i) and the equation:

d_A = \frac{(D + d)}{2}

$d_A$ = ______ $\text{cm}$

(iii)

Calculate a value for the capacity $V_1$ of the cup using the equation:

V_1 = \frac{\pi d_A^2 h}{4}

$V_1$ = ______ $\text{cm}^3$

(b)

method 2

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 $l$ of string used.

$l = 87.9\text{ cm}$

(i)

Calculate the average circumference $C$ of the cup.

$C$ = ______ $\text{cm}$

(ii)

Use your values of $h$ from (a)(i) and $C$ from (b)(i) to calculate a value for the capacity $V_2$ of the cup using the equation:

V_2 = \frac{C^2 h}{4\pi}

$V_2$ = ______ $\text{cm}^3$

(c)

method 3

The student:

fills a measuring cylinder with water, up to the 220 $\text{cm}^3$ 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 $R$ .

Fig. 1.2

(i)

Write down the new reading $R$ .

$R$ = ______ $\text{cm}^3$

(ii)

Determine the volume of water $V_3$ in the cup.

Show your working.

$V_3$ = ______ $\text{cm}^3$

(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 ______

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3 more questions

Q2Observations and Measurements · Experimental Contexts · Analysis, Conclusions and Evaluation · Use of Techniques, Apparatus and Materials10M
Q3Experimental Contexts · Observations and Measurements · Analysis, Conclusions and Evaluation14M
Q4Planning Experiments and Investigations · Experimental Contexts6M

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