Question

how many liters of paint must you buy to paint the walls of a rectangular prism - shaped room that is 16 m by 11 m with a ceiling height of 8 m? 1 l of paint covers 40 m²? (assume there are no doors or windows and paint comes in 1 - l cans.) the amount of paint needed is □ liters. (round up to the nearest integer as needed.)

Explanation:

Step1: Calculate the lateral surface area of the room

The room is a rectangular prism. The formula for the lateral surface area \(S\) of a rectangular prism is \(S = 2h(l + w)\), where \(l = 16m\), \(w=11m\), and \(h = 8m\).

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Step2: Calculate the amount of paint needed

Since 1 liter of paint covers \(40m^{2}\), the amount of paint \(n\) (in liters) is \(n=\frac{S}{40}\).

$$ n=\frac{432}{40}=10.8 $$

Since we can't buy a fraction of a liter and we need to have enough paint, we round up to the next - integer.

Answer:

11