The student uses a ruler and two rectangular wooden blocks to help him measure the external diameter $D$ of the test-tube. Describe, with the help of a diagram, how the student obtains an accurate value for $D$.
Find the height $h$ of the water in the full size test-tube in Fig. 1.1. Enter $h$ in centimetres, rounded to the nearest millimetre, in the second row of Table 1.1.
Enter $V_R$ in Table 1.1.
Calculate the volume $V$ of water in the test-tube. Put your answer into Table 1.1.
On the grid given, plot a graph of $V$ against $h$, with $V$ on the y-axis and $h$ on the x-axis. Begin both axes at the origin $(0,0)$. Then draw the best-fit straight line.
Calculate the gradient $m$ of your line. Show every step of your working and indicate on the graph the values you use.
If the test-tube is a perfect cylinder, then the internal diameter $d$ is found from $d = \sqrt{\frac{4m}{\pi}}$. Use your value of $m$ from (e)(i) together with the equation to calculate $d$.
State one difficulty in measuring the height $h$ of the water in the test-tube and suggest how that difficulty can be overcome.
Give another reason why your calculated value for $d$ is only approximate.
Measure the external diameter $D$ of the full size test-tube in Fig. 1.1. Record $D$ in centimetres to the nearest millimetre.
Use your answers for (e)(ii) and (g)(i) to calculate the thickness of the glass in the test-tube.