Physics 5054 · O Level · Physical quantities and measurement techniques

Physical quantities and measurement techniques — practice question

A student uses three different methods to find the capacity of a drinks cup. The capacity of a cup is the greatest volume of liquid it can contain.
(a(i))[2]

From the diagram, measure the cup's height $h$ and its diameters $D$ and $d$.

(a(ii))[1]

Calculate the average diameter $d_A$ of the cup from your readings in (a)(i) using the equation $d_A = \frac{D + d}{2}$.

(a(iii))[1]

Calculate a value for the cup's capacity $V_1$ using $V_1 = \frac{\pi d_A^2 h}{4}$.

(b(i))[1]

Calculate the average circumference $C$ for the cup.

(b(ii))[1]

Use the value of $h$ from (a)(i) together with $C$ from (b)(i) to calculate the cup's capacity $V_2$ using the equation $V_2 = \frac{C^2 h}{4\pi}$.

(c(i))[1]

State the new reading $R$.

(c(ii))[1]

Calculate the volume of water $V_3$ in the cup. Show your working.

(d)[2]

State one reason why the volume found in method 2 and one reason why the volume found in method 3 are not accurate.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $h=8.3\text{ cm}$, rounded to the nearest $0.1\text{ cm}$

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