Final answer:
To find the number of squares Kelly will need for the quilt, calculate the total area of the quilt and the area of each square. Kelly needs approximately 271 squares for her quilt.
Step-by-step explanation:
In order to determine the number of squares Kelly needs to make for her quilt, we must first calculate the total area of the quilt and then divide this area by the area of each square.
The quilt is designed to be a rectangle with dimensions of 7ft 4in by 6ft 5in. To find the total area, we need to multiply the length by the width.
Total Area = Length × Width
Total Area = 7ft 4in × 6ft 5in
Before performing the multiplication, we need to convert the feet and inches to inches. There are 12 inches in a foot, so:
7ft 4in = (7 × 12) + 4 = 84 + 4 = 88 inches
6ft 5in = (6 × 12) + 5 = 72 + 5 = 77 inches
Now we can find the total area of the quilt:
Total Area = 88 inches × 77 inches = 6756 square inches
Next, we need to determine the area of each square. Since Kelly is sewing a circle on top of each square, we can assume the squares have a uniform size. Let’s call the side length of each square “s”. Since the circle is sewn on top of the square, the area of each square is the area of the circle minus the area of the circle’s interior.
Area of Square = πr² - π(r² - r) Area of Square = πr² - πr Area of Square = πr(2r - 1)
Let’s assume the radius of each circle is “r”. Since the quilt is designed to be a rectangle, the radius of each circle can be half the side length of the square. So, r = s/2.
Now we can rewrite the formula for the area of the square using the side length “s”:
Area of Square = π(s/2)²(2(s/2) - 1)
Area of Square = π(s²/4)(2s/2 - 1)
Area of Square = πs²/4
Now we can find the number of squares Kelly needs by dividing the total area of the quilt by the area of each square:
Number of Squares = Total Area / Area of Square
Number of Squares = 6756 square inches / (πs²/4)
To simplify the equation, let’s assume π ≈ 3.14.
Number of Squares ≈ 6756 square inches / (3.14 × s²/4)
Number of Squares ≈ 6756 × 4 / (3.14 × s²)
Number of Squares ≈ (6756 × 4) / 3.14s²
Number of Squares ≈ 27024 / 3.14s²
Since Kelly needs to round the answer to the nearest tenth, we can calculate the value of “s” that makes the number of squares approximately 270.
s² ≈ (270 × 3.14) / 27024 ≈ 0.94
s ≈ √0.94 ≈ 0.97
Based on this calculation, Kelly would need approximately 271 squares for her quilt.