Subjects algebra

Paint Needed E4D5A0

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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