Devon’s bike has wheels that are 27 inches in diameter. After the front wheel picks up a tack, Devon rolls another 100 feet and stops. How far above the ground is the tack?
To find the height of the tack above the ground, we first need to calculate the distance traveled by the front wheel after picking up the tack.
We know the diameter of the wheel, which is 27 inches. Since the circumference of a circle is given by the formula C = πd (where d is the diameter), we can find the circumference of the front wheel by multiplying its diameter by π:
C = πd = π * 27 inches.
Next, we need to convert the distance traveled by the wheel after picking up the tack from feet to inches. There are 12 inches in a foot, so 100 feet is equal to 100 * 12 inches.
Now, we have the circumference of the wheel in inches and the distance traveled by the wheel after picking up the tack in inches. We can use this information to find the number of complete rotations made by the wheel by dividing the distance traveled by the circumference of the wheel:
Number of rotations = distance traveled / circumference of the wheel.
After finding the number of rotations, we can calculate the height of the tack above the ground. Since every complete rotation of the wheel corresponds to one circumference, the height of the tack would be the remaining distance covered by the wheel after completing the rotations.
Let's calculate step by step:
1. Calculate the circumference of the front wheel:
Circumference = π * 27 inches.
2. Convert the distance traveled by the wheel after picking up the tack from feet to inches:
Distance traveled = 100 feet * 12 inches/foot.
3. Find the number of rotations made by the wheel:
Number of rotations = Distance traveled / Circumference.
4. Calculate the remaining distance covered by the wheel after completing the rotations:
Remaining distance = Circumference - (Number of rotations * Circumference).
Therefore, the height of the tack above the ground would be equal to the remaining distance covered by the wheel after completing the rotations.