1. **State the problem:** Calculate the total wall area of a room, estimate the paint needed, and compute the total cost of the paint.
2. **Formula for wall area:** The total wall area $A$ of a rectangular room is given by
$$A = 2h(l + w)$$
where $h$ is the height, $l$ is the length, and $w$ is the width of the room.
3. **Paint needed:** Since 1 liter covers 10 m², the paint required $P$ in liters is
$$P = \frac{A}{10}$$
4. **Cost calculation:** If paint costs 350 per liter, the total cost $C$ is
$$C = 350 \times P$$
5. **Example calculation:** Suppose the room dimensions are $h=3$ m, $l=5$ m, and $w=4$ m.
6. Calculate wall area:
$$A = 2 \times 3 \times (5 + 4) = 2 \times 3 \times 9 = 54\text{ m}^2$$
7. Calculate paint needed:
$$P = \frac{54}{10} = 5.4\text{ liters}$$
8. Calculate total cost:
$$C = 350 \times 5.4 = 1890$$
**Final answer:**
- Total wall area: 54 m²
- Paint required: 5.4 liters
- Total cost: 1890
Paint Needed E4D5A0
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.