Surface Area of a Cuboid: Worded problems

To solve this problem, we'll proceed as follows:

• Step 1: Identify the box dimensions and list them as length $l = 20 \, \text{cm}$, width $w = 30 \, \text{cm}$, and height $h = 70 \, \text{cm}$.
• Step 2: Use the surface area formula for a cuboid:
  $A = 2(lw + lh + wh)$
• Step 3: Calculate the individual areas:
  - Base: $lw = 20 \times 30 = 600 \, \text{cm}^2$
  - Front: $lh = 20 \times 70 = 1400 \, \text{cm}^2$
  - Side: $wh = 30 \times 70 = 2100 \, \text{cm}^2$
• Step 4: Compute the total surface area in cm²:
  $A = 2(600 + 1400 + 2100) = 2 \times 4100 = 8200 \, \text{cm}^2$
• Step 5: Convert to square meters (since $1 \, \text{m}^2 = 10,000 \, \text{cm}^2$):
  $8200 \, \text{cm}^2 = \frac{8200}{10000} = 0.82 \, \text{m}^2$

Thus, Ezequiel needs $0.82 \, \text{m}^2$ of wrapping paper.

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 $0.5 \text{ meters}$.