How much paint is needed to paint the walls of a room 16 x 12 x 10 each gallon covers 400 square feet in each quart covers 100 square feet?

If you buy in gallon cans, then you need 2 gallons.

If you buy in quarts, then you need 6 quarts.

Work Shown:

I'm assuming this room has 10 ft ceilings. So the length and width of the room is 16 ft by 12 ft. Two walls are 16*10 = 160 square feet each, so we have 2*160 = 320 sq ft so far. Then we have another two walls that are 12*10 = 120 sq ft, giving an additional 2*120 = 240 sq ft. In total, the walls cover 320+240 = 560 sq ft.

The walls are the lateral surface area of the rectangular block that the room forms. You can use this formula

LSA = 2*(L*H + W*H)

to find the lateral surface area (LSA). In this case, L = 16, W = 12, H = 10.

Because 1 gallon of paint covers 400 square feet, we can divide the lateral surface area by 400 to find out how many gallons of paint we need.

560/400 = 1.4

round this up to 2 gallons so we have enough paint. If we round to 1 gallon, then we'll be short of the paint needed (we'll be missing that 0.4 of a gallon).

At the same time, 1 quart of paint covers 100 sq ft, so

560/100 = 5.6

which rounds up to 6. Therefore, we need 6 quarts of paint.

Another way to get this is to multiply 1.4 by 4

1.4*4 = 5.6

because there are 4 quarts in a gallon. This is evident by how 400 is 4 times that of 100.

It might be tempting to round 1.4 up to 2, then multiply by 4 to get 2*4 = 8, which may seem we need 8 quarts instead of 6. This is a bit too much as 6 quarts works also. The value 6 is the smallest whole number of quarts we can buy and still cover all four walls with paint.