A mountain bike tire has a diameter of 26 inches. To the nearest foot, how far does the tire travel when it makes 32 revolutions?
To find out how far a mountain bike tire travels in 32 revolutions, we need to know the circumference of the tire. The circumference is the distance all the way around the tire.
The formula to calculate the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.
In this case, the diameter of the tire is given as 26 inches. So we can calculate the circumference as follows:
C = π * 26 inches
Now we need to convert the circumference from inches to feet because we want the answer to the nearest foot. Since there are 12 inches in a foot, we can divide the circumference in inches by 12 to get the circumference in feet.
C in feet = (π * 26 inches) / 12 inches
Once we have the circumference in feet, we can find out the distance traveled by multiplying it by the number of revolutions:
Distance traveled = C in feet * number of revolutions
Now let's plug in the values and calculate:
C in feet = (π * 26 inches) / 12 inches = (3.14 * 26) / 12 ≈ 6.854 feet (rounded to three decimal places)
Distance traveled = 6.854 feet * 32 revolutions
Calculating further:
Distance traveled ≈ 219.328 feet (rounded to three decimal places)
Therefore, the mountain bike tire travels approximately 219 feet when it makes 32 revolutions.
To find the distance traveled by the tire, we need to find the circumference of the tire first.
The formula for the circumference of a circle is: C = π * d, where C is the circumference and d is the diameter of the circle.
Given that the diameter of the mountain bike tire is 26 inches, we can calculate the circumference:
C = π * 26 inches
C ≈ 81.68 inches
Now, to find the distance traveled when the tire makes 32 revolutions, we can calculate the total distance:
Distance = Circumference * Number of revolutions
Distance = 81.68 inches * 32 revolutions
Distance ≈ 2,613.76 inches
To convert inches to feet, divide the distance by 12 (since there are 12 inches in a foot):
Distance in feet = 2,613.76 inches / 12
Distance ≈ 217.81 feet
Therefore, to the nearest foot, the mountain bike tire travels approximately 218 feet when it makes 32 revolutions.
circumference = 2 pi r
= 2 *3.14159* 26 inches
goes 32 * circumference /12 feet