Surface Area Calculation: Finding Container Width Using Paint Coverage of 1/3 Liter per m²

To solve this problem, we'll follow these steps:

• Step 1: Calculate the total painted surface area using the paint volume and coverage.
• Step 2: Set up the equation using the dimensions of the container and solve for width.

Now, let's work through each step:

Step 1: Calculate the total painted surface area
Given that Soledad uses $35\frac{1}{3}$ liters of paint, which is $\frac{106}{3}$ liters, and each liter covers $\frac{1}{3}$ square meters, the total painted surface area is:

$\text{Total Surface Area} = \left(\frac{106}{3}\right) \times 3 = 106 \text{ square meters}$

Step 2: Formulate the equation for the painted surface area
The surface area painted includes the two sides ($2(h \cdot l)$), two ends ($2(h \cdot w)$), and the top ($l \cdot w$) minus the bottom ($l \cdot w$).
The equation for the total surface area becomes:

$2(4 \cdot 12) + 2(4 \cdot w) + (12 \cdot w) = 106$

Simplifying the equation:

$96 + 8w + 12w = 106$

$96 + 20w = 106$

Solving for $w$:

$20w = 106 - 96$

$20w = 10$

$w = \frac{10}{20} = 0.5 \text{ meters}$

Therefore, the width of the container is $0.5 \text{ meters}$.