I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?

Question

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall?

Answer 1

First, convert the dimensions of the wall to meters by multiplying by $0.3048$: $15$ meters = $15 \times 0.3048 = 4.572$ meters, $60$ meters = $60 \times 0.3048 = 18.288$ meters.

Now we can find the area of the wall in square meters: $4.572 \text{ meters}\times 18.288 \text{ meters} = 83.432896 \text{ square meters}$.

Since one gallon of paint covers $400$ square feet, which is $400 \times 0.3048^2 \text{ square meters} \approx 37.16$ square meters, we need at least $\dfrac{83.432896}{37.16}=\boxed{2}$ gallons of paint.