Estimating Wall Paint
A homeowner wants to paint the four walls of a rectangular room that is 5 m long, 4 m wide, and 2.5 m high. There is one door of area 2 m² and two windows each of area 1.5 m² that will not be painted. Paint is sold in 4-litre cans, and each litre covers 12 m² per coat. The homeowner plans to apply two coats of paint. She needs to buy whole cans and wants to minimize waste while ensuring enough paint. She also wants to know the total cost if each can costs $45.
1. Calculate the total area to be painted (the four walls minus door and windows). Show your working.
Read the worked answer
The area of the four walls is the perimeter of the room multiplied by the height. Perimeter = 2*(5+4) = 18 m. Wall area = 18 * 2.5 = 45 m². Subtract door and windows: door area = 2 m², two windows = 2*1.5 = 3 m². Total openings = 5 m². Paintable area = 45 - 5 = 40 m².
2. Determine the number of 4-litre cans needed for two coats, and the total cost. Explain your reasoning, including any assumptions about coverage.
Read the worked answer
Each litre covers 12 m², so one 4-litre can covers 412 = 48 m² per coat. For two coats, total coverage needed = 40 m² * 2 = 80 m². Number of cans = ceil(80 / 48) = ceil(1.666...) = 2 cans. Check: two cans provide 248 = 96 m² per coat? Wait, careful: Each can covers 48 m² for one coat. For two coats, we need enough paint for 80 m² total (since two coats means painting the 40 m² twice). So total paint volume needed = (80 m²) / (12 m²/L) = 6.666... L. Since each can is 4 L, number of cans = ceil(6.666/4) = ceil(1.666) = 2 cans. Two cans give 8 L, which covers 8*12 = 96 m², enough for 80 m². So 2 cans. Cost = 2 * $45 = $90. Assumption: coverage rate is exact and no extra paint is needed for edges or absorption; if coverage is less, might need more, but based on given rate, 2 cans suffice.