# The floor of a room is covered with a carpet with a 2-color design. The room is square shaped. Each side has 12 ft.The red circle of the carpet, whose center is in the center of the room, leaves 2...

The floor of a room is covered with a carpet with a 2-color design. The room is square shaped. Each side has 12 ft.

The red circle of the carpet, whose center is in the center of the room, leaves 2 ft of white carpet to each of the 4 walls. The red carpet costs $12/sqft and the white carpet costs $10/sqft. How much will cost the carpet (red and white)?

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The room has 12 ft sided square floor

The capet has a circular red part in the centre which leaves 2ft on each side from the floor. From this we decide that the red circular part of carpet has a diameter 12-2-2 = 8 feet or a radius r = 8/2 = 4ft.

The area of red part of carpet = 4pi* r^2 = 4*pi*4^2 = 64pi sq ft.

So the area of white part of the carpet = Area of the room - area of read cicular part = (144-64pi)sq ft

There the cost of red part of carpet @ $12 /sq ft = $12*64pi

The cost of white part of the carpet (@ $10/sqft = 10*(144-64pi)

Therefore the total cost of carpet = ${12*64pi+10(144-64pi) } = ${1440 +(12-10)64pi }= ${1440+128pi }= $1842.12386

First, we'll evaluate the area of the room. Since the room is a square, the area is:

A = 12ft*12ft

A = 144 ft^2

We'll use now the 2 given prices and we'll calculate:

144ft^2 * $10/ft^2 = $1440

144ft^2 * $12/ft^2 = $1728

Now, we'll determine the diameter of the red carpet, circle shaped. Since we have 2ft to each wall, the diameter will be:

D = 12 - 4

D = 8 ft

r = 8/2 ft

r = 4 ft

The area of the red circle is:

A = pi*r^2

A = 3.14*16

A of red carpet = 50.24 ft^2

The cost of the red carpet is:

50.24 ft^2 * $12/ft^2 = $602.88

The area of the white carpet is:

144 ft^2 - 50.24 ft^2 = 93.76 ft^2

The cost of the white carpet is:

93.76 ft^2 * $10/ft^2 = $937.60

**The total cost of the entire carpet is:**

**$602.88 + $937.60 = $1540.48**

The first step is to determine the entire area of the square room.

12 ' * 12' = 144 ft. sq.

The cross section of the center circle is 12 ft - 2 ft on the left and -2 ft on the right giving a diameter of 8 ft.

the area of a circle is pi * (d/2)^2. For this problem pi * (8/2)^2

pi * 4^2

pi*16=50.24 ft^2

Subtracting this area from the total area

144-50.24 = 93.76 ft^2

To determine cost for each part

50.24 * $12= $602.88 red

93.76 * $10= $937.60 white

Sum together to get total cost

$602.88 + $937.60 = $1,540.48