If a rubber band can be stretched to a circular shape that has a radius of 3.3 inches. How many 1.1 - mm diameter toothpicks of could fit within it? (1 inch = 25.4 mm)
To determine how many toothpicks could fit within the circular shape of the stretched rubber band, we need to calculate the circumference of the circle and divide it by the circumference of a toothpick.
First, let's convert the diameter of the toothpick from millimeters to inches. We know that 1 inch is equal to 25.4 mm, so the diameter of the toothpick in inches is 1.1 mm divided by 25.4, which is approximately 0.0433 inches.
The circumference of a circle is given by the formula: C = 2πr, where C represents the circumference and r represents the radius.
Using the given radius of 3.3 inches, we can calculate the circumference of the circle:
C = 2 × π × 3.3
C ≈ 20.734 inches
Now, we can divide the circumference of the circle by the circumference of a toothpick to find how many toothpicks could fit within it:
Number of toothpicks = Circumference of circle ÷ Circumference of toothpick
Number of toothpicks ≈ 20.734 ÷ 0.0433
Number of toothpicks ≈ 479.205
Therefore, approximately 479 toothpicks could fit within the circular shape of the stretched rubber band.
To calculate the number of toothpicks that could fit within the circular shape formed by the rubber band, we need to find the circumference of the circle and divide it by the diameter of the toothpick.
1. First, let's calculate the circumference of the circle formed by the rubber band. The formula for the circumference of a circle is C = 2πr, where r is the radius.
Plugging in the given radius of 3.3 inches:
C = 2π(3.3) = 6.6π inches
2. Next, we need to convert the circumference from inches to millimeters because the diameter of the toothpick is given in millimeters.
Since 1 inch is equal to 25.4 millimeters, we multiply the circumference by 25.4 to convert it to millimeters:
C = 6.6π * 25.4 = 166.44π millimeters
3. Now, let's calculate the diameter of the toothpick in millimeters. We know that 1 inch is equal to 25.4 millimeters.
The diameter of the toothpick is given as 1.1 millimeters.
4. To find how many toothpicks can fit within the circular shape, we divide the circumference by the diameter of the toothpick:
Number of toothpicks = (Circumference of circle) / (Diameter of toothpick)
Number of toothpicks = 166.44π / 1.1
Therefore, the number of 1.1-mm diameter toothpicks that could fit within the circular shape formed by the rubber band is approximately 47.92π (or 150.91) toothpicks.