Question

to paint the walls of a rectangular room that is 10 meters long, 8 meters wide, and 2.5 meters high with two coats of paint, if one liter of paint covers 10 sq m, how many liters are needed?
a. 144
b. 72
c. 36
d. 18

Explanation:

Step1: Calculate the area of the four walls

The formula for the lateral surface area of a rectangular prism (room walls) is \(2\times(\text{length}\times\text{height}+\text{width}\times\text{height})\).
Substitute length \(l = 10\)m, width \(w=8\)m, height \(h = 2.5\)m.

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Step2: Calculate the area for two - coat painting

Since there are two coats of paint, the total area \(A_{total}=2\times A\).
\(A_{total}=2\times90 = 180\space m^{2}\)

Step3: Calculate the amount of paint needed

Given that one liter of paint covers \(10\space m^{2}\). Let the amount of paint be \(V\).
Using the formula \(V=\frac{A_{total}}{\text{coverage per liter}}\), substitute \(A_{total}=180\space m^{2}\) and coverage per liter \( = 10\space m^{2}/L\)
\(V=\frac{180}{10}=18\space L\)

Answer:

d. 18