A metal bar measures 10cm by 5cm by 4 cm and has a mass of 3.6 kg. Deduce if the metal is pure gold by finding its density in g/cm3. (density of pure gold is 19.3g/cm3)

It has a density of 18 g/cm³, which makes it not pure gold.

You find density by dividing mass by volume (m/V), but first in this case you should convert kg to g by multiplying the mass by 1000, which gives you 3600 g (3.6 x 1000 = 3600). Then you need to find the volume, which you can do by multiplying all the side lengths together (because this is a rectangular prism), which gives you 200 cm³. Then you can divide mass by volume.

3600 g/200 cm³ = 18 g/cm³, which is sadly not 19.3 so its not pure gold