if a rubber band can be stretched to a circular shape that has a radius of 3.4 inches. how many 1.3-mm diameter toothpicks could of fit within it? (1 inch = 25.4 mm)
ignoring the grammar mistakes, and noting that since the diameter of the toothpicks is small, we can assume they fill "all" the interior, then we can squeeze
(3.4*25.4)^2/(1.3)^2 = 4413 toothpicks into the band
To find out how many toothpicks can fit within the circular shape formed by the rubber band, we need to calculate the circumference of the circle and then divide it by the width of a toothpick. Here's how you can do it:
1. First, we need to convert the radius of the circular shape from inches to millimeters. Since 1 inch equals 25.4 mm, the radius of the circular shape is 3.4 inches * 25.4 mm/inch = 86.36 mm.
2. Next, we need to calculate the circumference of the circle using the formula C = 2πr, where C is the circumference and r is the radius. Substituting the values, we have C = 2 * π * 86.36 mm.
3. Now we need to convert the diameter of the toothpick from millimeters to inches. The diameter is given as 1.3 mm, so the diameter in inches is 1.3 mm / 25.4 mm/inch = 0.0512 inches.
4. Finally, we can find out how many toothpicks can fit within the circular shape by dividing the circumference (in millimeters) by the width of a toothpick (in inches). So, the number of toothpicks that can fit is C / 0.0512.
By following these steps and plugging in the appropriate values, you can calculate the precise number of toothpicks that can fit within the circular shape defined by the rubber band.