April wants to add a ribbon border to the circular rug in her living room. If the area of her rug is 113.04 square feet, how long does the ribbon need to be?
since a = pi r^2,
113.04 = 3.14 r^2
r = 6 ft
since c = 2pi*r
c = 2*3.14*6
c = 37.68 ft
i35
To find out how long the ribbon needs to be, we need to determine the circumference of the circular rug.
The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
Given that the area of the rug is 113.04 square feet, we can rearrange the formula to solve for the radius:
A = π * r^2
113.04 = π * r^2
Next, we divide both sides of the equation by π to isolate r^2:
r^2 = 113.04 / π
Using a calculator, we can approximate π to be 3.14159. So:
r^2 = 113.04 / 3.14159
Now, we can take the square root of both sides to find the radius:
r = √(113.04 / 3.14159)
r ≈ 5.35
Therefore, the radius of the circular rug is approximately 5.35 feet.
Now, to find the circumference of the rug, we use the formula C = 2 * π * r:
C = 2 * 3.14159 * 5.35
C ≈ 33.67
Hence, the length of the ribbon needs to be approximately 33.67 feet to go around the circular rug.