Question

an empty paint tin of diameterv0.150m and height0.120m has amass of 0.22 kg it is filled with paint to within 7mm of the top its total mass is then 6.50kg calculate for the paint in the tin the mass the volume and the density

Answer 1

`\large \boxed{\text{3140 kg$\cdot$m}^(-3)}`

Step-by-step explanation:

`\text{Density} = \frac{\text{mass}}{\text{volume}}\\\\\rho = (m)/(V)`

1. Mass of paint

`\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}`

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

`\begin{array}{rcl}V & = & \pi r^(2)h \\& = & \pi * (\text{0.0750 m})^(2) * \text{0.113 m}\\& = & 2.002 * 10^(-3)\text{ m}^(3)\\\end{array}`

3. Density of paint

`\rho = \frac{\text{6.28 kg}}{2.002 * 10^(-3)\text{ m}^(3)} = \textbf{3140 kg$\cdot$m}^(-3)\\\\\text{The density of the paint is $\large \boxed{\textbf{3140 kg$\cdot$m}^{\mathbf{-3}}}$}`