JAMB Physics 2013 Paper

Concept:Mass is obtained by multiplying density by volume.When two substances have the same mass, their densities and volumes are related by $m = \rho V$.Explanation:First, find the mass of the given petrol.The volume of petrol is $V_p = 4.2\ \mathrm{m}^3$.The density of petrol is $\rho_p = 7.2 \times 10^2\ \mathrm{kg\,m^{-3}}$.So, $m_p = \rho_p \times V_p = (7.2 \times 10^2)(4.2) = 3024\ \mathrm{kg}$.Since the alcohol must have the same mass, $m_a = 3024\ \mathrm{kg}$.The density of alcohol is $\rho_a = 8.4 \times 10^2\ \mathrm{kg\,m^{-3}}$.Using $V_a = \frac{m_a}{\rho_a}$, we get $V_a = \frac{3024}{8.4 \times 10^2}$.This gives $V_a = \frac{3024}{840} = 3.6\ \mathrm{m}^3$.Answer:The volume of alcohol required is $3.6\ \mathrm{m}^3$.Therefore, the correct option is C.