A student measures the rise h of water in five tubes of different bore…

Step 1. The slope. $\dfrac{37.0\ \text{mm} - 18.5\ \text{mm}}{2.50\ \text{mm}^{-1} - 1.25\ \text{mm}^{-1}}$ $= 14.8\ \text{mm}^2$.

Step 2. The surface tension. The slope is $\dfrac{2T}{\rho g}$. We want $T$, so $T = \dfrac{\rho g \times \text{slope}}{2}$ $= \tfrac{1}{2} \times 998\ \text{kg/m}^3$ $\times 9.8\ \text{m/s}^2$ $\times 14.8 \times 10^{-6}\ \text{m}^2$ $= 0.0724\ \text{N/m}$.

Step 3. The radius. $h r = 14.8\ \text{mm}^2$, so $r = \dfrac{14.8\ \text{mm}^2}{22.0\ \text{mm}} = 0.673$ mm.