Answer:
[tex]\large \boxed{\text{3140 kg$\cdot$m}^{-3}}[/tex]
Explanation:
[tex]\text{Density} = \dfrac{\text{mass}}{\text{volume}}\\\\\rho = \dfrac{m}{V}[/tex]
1. Mass of paint
[tex]\begin{array}{rcl}\text{Mass of paint} & = & \text{mass of (paint + can) - mass of can}\\& = & \text{6.50 kg - 0.22 kg}\\& = & \text{6.28 kg}\\\end{array}[/tex]
2. Volume of paint
The paint is contained in a cylinder.
V = πr²h
(a) Radius of can
r = d/2 = (0.150 m)/2 = 0.0750 m
(b) Height of paint
h = 0.120 m - 0.007 m = 0.113 m
(c) Volume of paint
[tex]\begin{array}{rcl}V & = & \pi r^{2}h \\& = & \pi \times (\text{0.0750 m})^{2} \times \text{0.113 m}\\& = & 2.002 \times 10^{-3}\text{ m}^{3}\\\end{array}[/tex]
3. Density of paint
[tex]\rho = \dfrac{\text{6.28 kg}}{2.002 \times 10^{-3}\text{ m}^{3}} = \textbf{3140 kg$\cdot$m}^{-3}\\\\\text{The density of the paint is $\large \boxed{\textbf{3140 kg$\cdot$m}^{\mathbf{-3}}}$}[/tex]
