To determine how many liters of paint will be needed, we need to follow these steps:
1. Calculate the Total Area to Be Painted:
- Prudence wants to paint three coats of paint over an area of [tex]\( 14.42 \, m^2 \)[/tex].
- Since she plans to apply three coats, the total area that needs to be painted will be three times the single coat area.
[tex]\[
\text{Total area} = \text{coats of paint} \times \text{area to cover} = 3 \times 14.42 \, m^2 = 43.26 \, m^2
\][/tex]
2. Calculate the Number of Liters Required:
- We know that one liter of paint covers [tex]\( 8 \, m^2 \)[/tex].
- To find out how many liters are required to cover [tex]\( 43.26 \, m^2 \)[/tex], we divide the total area by the coverage per liter.
[tex]\[
\text{Liters needed} = \frac{\text{total area}}{\text{coverage per liter}} = \frac{43.26 \, m^2}{8 \, m^2/\text{liter}} = 5.4075 \, \text{liters}
\][/tex]
Therefore, Prudence will need approximately 5.4075 liters of paint to apply three coats over an area of [tex]\( 14.42 \, m^2 \)[/tex].
In summary:
- Total area to be covered for 3 coats: [tex]\( 43.26 \, m^2 \)[/tex]
- Liters of paint needed: [tex]\( 5.4075 \, \text{liters} \)[/tex]
