Question
A painter is going to paint a room shaped like a cube, with square walls that are 20 ft. on each side. A gallon of paint can be used to cover 400 square feet. How many gallons of paint should the painter buy if he is going to paint the four walls of the room? Responses
Answers
GPT-4o mini
To determine how many gallons of paint the painter needs, we first need to calculate the total area of the four walls of the cubic room.
Since the room is a cube with each side measuring 20 feet, the area of each wall is:
\[
\text{Area of one wall} = \text{side} \times \text{side} = 20 \text{ ft} \times 20 \text{ ft} = 400 \text{ square feet}
\]
There are four walls in a cube, so the total area of the four walls is:
\[
\text{Total area} = 4 \times \text{Area of one wall} = 4 \times 400 \text{ square feet} = 1600 \text{ square feet}
\]
Now we need to determine how many gallons of paint are required to cover this area. Since one gallon of paint covers 400 square feet, we can calculate the number of gallons needed as follows:
\[
\text{Gallons needed} = \frac{\text{Total area}}{\text{Area covered by one gallon}} = \frac{1600 \text{ square feet}}{400 \text{ square feet per gallon}} = 4 \text{ gallons}
\]
Therefore, the painter should buy **4 gallons of paint** to cover the four walls of the room.
Since the room is a cube with each side measuring 20 feet, the area of each wall is:
\[
\text{Area of one wall} = \text{side} \times \text{side} = 20 \text{ ft} \times 20 \text{ ft} = 400 \text{ square feet}
\]
There are four walls in a cube, so the total area of the four walls is:
\[
\text{Total area} = 4 \times \text{Area of one wall} = 4 \times 400 \text{ square feet} = 1600 \text{ square feet}
\]
Now we need to determine how many gallons of paint are required to cover this area. Since one gallon of paint covers 400 square feet, we can calculate the number of gallons needed as follows:
\[
\text{Gallons needed} = \frac{\text{Total area}}{\text{Area covered by one gallon}} = \frac{1600 \text{ square feet}}{400 \text{ square feet per gallon}} = 4 \text{ gallons}
\]
Therefore, the painter should buy **4 gallons of paint** to cover the four walls of the room.