Subjects algebra

Paint Cost Room

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Paint Cost Room


1. **State the problem:** We need to find the cost of painting the walls of a room with dimensions 4.38 m length, 3.74 m width, and 2.36 m height. The room has two doorways and three windows, and the painting cost is 74 per square meter. 2. **Calculate total wall surface area:** The room has 4 walls. Two walls have area length × height, and two have width × height. $$\text{Total wall area} = 2 \times (4.38 \times 2.36) + 2 \times (3.74 \times 2.36)$$ $$= 2 \times 10.3368 + 2 \times 8.8264 = 20.6736 + 17.6528 = 38.3264 \text{ m}^2$$ 3. **Calculate total area of doors:** Each door is 76 cm by 198 cm. Convert to meters: 0.76 m by 1.98 m. $$\text{Area per door} = 0.76 \times 1.98 = 1.5048 \text{ m}^2$$ Two doors: $$2 \times 1.5048 = 3.0096 \text{ m}^2$$ 4. **Calculate total area of windows:** Each window is 88 cm by 106 cm. Convert to meters: 0.88 m by 1.06 m. $$\text{Area per window} = 0.88 \times 1.06 = 0.9328 \text{ m}^2$$ Three windows: $$3 \times 0.9328 = 2.7984 \text{ m}^2$$ 5. **Calculate paintable wall area:** Subtract area of doors and windows from total wall area. $$\text{Paintable area} = 38.3264 - (3.0096 + 2.7984) = 38.3264 - 5.808 = 32.5184 \text{ m}^2$$ 6. **Calculate cost of painting:** Cost per square meter is 74. $$\text{Total cost} = 32.5184 \times 74 = 2406.3616$$ 7. **Round to nearest Naira:** $$\text{Total cost} \approx 2406$$ **Final answer:** The cost of painting the walls of the room is 2406 to the nearest Naira.