Shmikea, the newly imported Norwegian superstore, sells beautiful 6-foot round shag rugs. Borg's living room is a 12 by 18 foot rectangle, and his goal is to cover as much of the floor as possible with these rugs without them overlapping. How much of the floor will be left uncovered if he goes through with his plan? (Use the approximation pi=3.14)
A. 7.74 ft squared
B. 46.44 ft squared
C. 169.56 ft squared
D. 216 ft squared
(12 * 18) - 6 π 3^2
To find out how many 6-foot round shag rugs can fit in Borg's 12 by 18-foot rectangle living room without overlapping, we need to calculate the area of the rectangle and the area of each rug.
The area of the rectangle is calculated by multiplying the length and width:
Area of the rectangle = 12 ft * 18 ft = 216 ft squared.
The area of each rug is calculated using the formula for the area of a circle:
Area of each rug = pi * radius^2,
where the radius of a 6-foot round rug is half the diameter, so the radius is 6 ft / 2 = 3 ft.
Area of each rug = 3.14 * (3 ft)^2 = 28.26 ft squared (approx).
Now, we can calculate how many rugs can fit in the living room by dividing the area of the rectangle by the area of each rug:
Number of rugs = Area of the rectangle / Area of each rug = 216 ft squared / 28.26 ft squared ≈ 7.64 (approx).
Since Borg wants to cover as much of the floor as possible without any overlap, we can only fit 7 rugs in the living room.
To find out how much of the floor will be left uncovered, we need to subtract the combined area of the rugs from the area of the rectangle:
Uncovered area = Area of the rectangle - (Number of rugs * Area of each rug)
Uncovered area = 216 ft squared - (7 rugs * 28.26 ft squared) ≈ 7.74 ft squared.
Therefore, the answer is A. 7.74 ft squared.
To determine how much of the floor will be left uncovered, we need to calculate the total area of the rugs and subtract it from the area of Borg's living room.
First, let’s calculate the area of one rug. The rug is 6 feet in diameter, so its radius is half of that, which is 6 / 2 = 3 feet. The area of a circle is calculated using the formula: area = π * radius^2. Substituting the values, the area of one rug is approximately 3.14 * 3^2 = 28.26 ft².
Next, we need to determine how many rugs fit in Borg's living room. His living room is a rectangle with dimensions 12 by 18 feet, so the area is 12 * 18 = 216 ft².
To find out how many rugs fit in the room, we need to divide the area of the room by the area of one rug: 216 ft² / 28.26 ft² ≈ 7.63.
Since we want to cover as much of the floor as possible without overlapping, Borg can lay down a maximum of 7 complete rugs.
Now, let’s find out how much of the floor will be left uncovered. The total area covered by the rugs is 7 * 28.26 ft² = 197.82 ft².
Therefore, the amount of uncovered floor space is: 216 ft² - 197.82 ft² = 18.18 ft².
Since the question asks for the answer to be in square feet, we know that 18.18 ft² is the correct answer. Therefore, the option closest to this value is:
A. 7.74 ft²
So, the correct answer is A. 7.74 ft².