Ashley bought a circular rug for her room. the rug has a diameter of 9 feet. Her room is rectangular-shaped and measures 12 feet by 18 feet.
about how much of Ashley's room will not be covered by the circular rug?
Find the area of the rectangle.
Find the area of the circle
take the difference between the two answers.
To find out how much of Ashley's room will not be covered by the circular rug, we first need to calculate the area of the room and the area of the circular rug.
The area of a rectangle is found by multiplying its length by its width. In this case, Ashley's room measures 12 feet by 18 feet, so its area is 12 feet x 18 feet = 216 square feet.
The area of a circle is found by multiplying π (pi) by the radius squared. Since the diameter of the circular rug is given as 9 feet, we can find the radius by dividing the diameter by 2. So the radius of the rug is 9 feet / 2 = 4.5 feet.
Now, we can calculate the area of the circular rug by substituting the radius into the formula: π x (radius)^2 = π x (4.5 feet)^2 ≈ 3.14 x (4.5 feet)^2 ≈ 3.14 x 20.25 square feet ≈ 63.585 square feet (rounded to three decimal places).
Finally, to find out how much of Ashley's room will not be covered by the circular rug, we subtract the area of the circular rug from the area of the room: 216 square feet - 63.585 square feet ≈ 152.415 square feet (rounded to three decimal places).
Therefore, about 152.415 square feet of Ashley's room will not be covered by the circular rug.