Question

A gallon of latex paint can cover 400 square feet. How many

gallon containers of paint should be bought to paint two
coats on each wall of a rectangular room whose dimensions
are 14 feet by 18 feet? (Assume 8-foot ceilings.)

Answer 1

To find:-

• The amount of paint required to paint two coats on the wall of a rectangular room of dimensions 14ft × 18ft × 8ft .

Answer:-

We are here given that 1 gallon of paint can be used to paint 400 sq ft. of an area .

There are 4 walls in a room and the area of opposite walls are equal.

So let's find out the area of wall ABCD , its area would be equal to the area of the wall EFGH . So ,

Area of wall ABCD and EFGH :-

Area = lb

Area = 18ft * 8ft

Area = 144ft.²

Therefore area of wall EFGH will also be 144ft.² .

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Again,

Area of wall DAHE and CBGF :-

Here both the areas of the wall would again be equal, as they have same dimensions of 14ft × 8ft .

Area = lb

Area = 14ft * 8ft

Area = 112ft.²

Therefore area of walls DAHE and CBGF is 112ft.²

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Calculating total area of the four walls :-

Total area = 2( 112ft.² + 144ft.² )= 512ft.²

Hence total area of four walls is 512ft.²

Now since there will be two coats of paints , total area to be painted would become double that is 1024ft.²

Now we may use Unitary Method :-

To paint 400ft.² 1 gallon of paint is needed.

To paint 1ft.² 1/400 gallon of paint is needed.

To paint 1024ft.² , 1/400*1024 = 2.56 gallons of paint would be needed.

Hence the total paint required is 2.56 gallons.

and we are done!

Answer 2

3 one-gallon containers of paint.

Explanation:

First, find the total surface area that needs to be painted.

To find the surface area of the walls of a rectangular room, calculate the area of each of the four walls and then add them together.

The area of a rectangle is the product of its width and length.

For the walls of the given room, the "length" is the height of 8 ft, since we want to paint from the floor to the ceiling.

The room has four walls:

• Two walls with dimensions 14 ft × 8 ft
• Two walls with dimensions 18 ft × 8 ft

Therefore, the total surface area is:

`\begin{aligned}\textsf{Total surface area}&=2(14 * 8)+2(18 * 8)\\&=2(112)+2(144)\\&=224+288\\&=512\;\sf ft^2\end{aligned}`

Since we want to apply two coats of paint, we need to double the surface area:

`\implies 2 * 512=1024 \; \sf ft^2`

Now, we can find how many gallons of paint are needed by dividing the total surface area by the coverage per gallon:

`\implies (1024)/(400)=2.56\; \sf gallons`

Therefore, we need 2.56 gallons of paint to paint two coats of each wall of the rectangular room.

Since we cannot buy a fraction of a gallon, we need to round up to the nearest gallon. Therefore, we need to buy 3 one-gallon containers of paint.