The total surface area, S, (measured in m2

) of n metal particles of radius r (measured in m) is given by the equation S = 4πnr2

.

The number of particles, n, is linked to the mass of one particle, m (in kg) and the total mass of metal, M (also in kg), by the equation M = nm.

The mass m (in kg) of one particle is related to its volume V

(m3

) and the density of the metal ρ (measured in kg m−3

) by the equation

ρ =

m V

.

Note that m (in a roman font) means metres, but m (in an italic font)

means mass. Be careful not to get confused.

The volume V (measured in m3

) of a particle is given by V =

4 3

πr 3

, where the r is the radius (in m).

a. Find an equation for the total surface area of these metal particles, in terms of the total mass of metal, the density of the metal and the radius, only.

b. Check that the units work out correctly in your answer