There are 1760 yards in a mile. A certain wheel makes 17600 revolutions in 40 miles. What is the number of yards in the radius of the wheel?Give the answer as a decimal to the nearest tenth of a yard.
To find the number of yards in the radius of the wheel, we can use the information given about the number of revolutions the wheel makes in 40 miles. Let's break down the steps:
Step 1: Calculate the total number of yards covered by the wheel in 40 miles.
Since there are 1760 yards in a mile, we multiply the number of miles (40) by the number of yards in a mile (1760).
Total yards covered = 40 miles * 1760 yards/mile = 70,400 yards
Step 2: Calculate the distance covered by each revolution of the wheel.
To find the distance covered by each revolution, we divide the total number of yards (70,400) by the number of revolutions (17,600).
Distance covered per revolution = 70,400 yards / 17,600 revolutions = 4 yards
Step 3: Determine the circumference of the wheel.
The circumference of a circle is equal to 2π multiplied by the radius (C = 2πr). Since we want the radius in terms of yards, let's rearrange the equation:
C = 2πr
r = C / (2π)
Step 4: Calculate the radius of the wheel in yards.
Since we know the distance covered per revolution is 4 yards (from Step 2), we substitute this value into the equation for the circumference (C = 4 yards):
r = 4 yards / (2π)
Step 5: Simplify the expression and round the result to the nearest tenth of a yard.
Using a calculator, we can evaluate the expression for the radius:
r ≈ 0.6366 yards ≈ 0.6 yards
Therefore, the number of yards in the radius of the wheel is approximately 0.6 yards (rounded to the nearest tenth of a yard).