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 find out how many toothpicks can fit within the circular shape formed by the stretched rubber band, we need to calculate the circumference of the circle and then divide it by the circumference of a toothpick.
Let's first calculate the circumference of the circular shape:
Circumference = 2 * π * Radius
Given that the radius is 3.3 inches, the circumference can be calculated as:
Circumference = 2 * π * 3.3 inches
Now, let's convert the circumference from inches to millimeters since the toothpick diameter is given in millimeters:
Circumference_in_millimeters = Circumference * 25.4 mm/inch
Next, we need to calculate the circumference of a toothpick. The diameter is given as 1.1 mm, so the circumference can be calculated as:
Circumference_of_toothpick = π * Diameter
Now, let's calculate the number of toothpicks that can fit within the circular shape:
Number_of_toothpicks = Circumference_in_millimeters / Circumference_of_toothpick
Finally, we can substitute the values and calculate the answer:
Number_of_toothpicks = (2 * π * 3.3 inches * 25.4 mm/inch) / (π * 1.1 mm)
Simplifying the equation:
Number_of_toothpicks = (2 * 3.3 * 25.4) / 1.1
Number_of_toothpicks = 150.12
Therefore, approximately 150 toothpicks could fit within the circular shape formed by stretching the rubber band.