This figure represents a design that is sewn onto a quilt square. The semicircles are a solid green fabric and the square is a floral fabric. The area of the solid green fabric is 8π square inches.
What percent of the design is floral fabric?
Use 3.14 for π. Round your answer to the nearest whole percent.
To find the total area of the design, we need to add the area of the solid green fabric (8π) to the area of the square it is sewn onto.
Let's assume the side length of the square is equal to x. The area of the square is x^2.
Given that the area of the solid green fabric is 8π, we have:
8π = πr^2
8 = r^2
r = 2
So, the square has a side length of 2 inches, and the total area of the design is 8π + 2^2 = 8π + 4.
To find the percentage of the design that is floral fabric, we can calculate the area of the floral fabric and then find the percentage as:
(4 / (8π + 4)) * 100
(4 / (8π + 4)) * 100 ≈ (4 / (8 * 3.14 + 4)) * 100 ≈ (4 / (25.12 + 4)) * 100 ≈ (4 / 29.12) * 100 ≈ 13.74%
Therefore, approximately 14% of the design is floral fabric.