Question

Density is defined as mass per unit volume. A solid cylinder has a diameter of 17.4 mm and a length of 50.3 mm. Its mass is 49 g. What is its density? Give your answer in metric tonnes per cubic metre. (The metric tonne is 1000 kg.)


Enter your answer as a number, using the appropriate number of sig figs. Do NOT include units*.


Density = _____

Answer 1

Calculate the volume, but first remember that 1 mm is $1\cdot10^{-3}$ m:

$$V=AH=\bigg(\frac{\pi d^2}{4}\bigg)H=\\ \space\\=\bigg(\frac{\pi (17.4\cdot10^{-3})^2}{4}\bigg)\cdot50.3\cdot10^{-3}=1.20\cdot10^{-5}\text{ m}^3.$$

Convert grams to tonnes. 1 g is 0.001 kg, one kg is 0.001 tonne. Therefore, the densoty is

$$\rho=\frac{m}{V}=\frac{49\cdot10^{-6}}{1.20\cdot10^{-5}}=4.10\text{ tonne/m}^3$$