distance covered by the larger wheel = 60(6Ï€) = 360Ï€ inches
so the smaller wheel with a circumference of 5Ï€ must cover the same distance
number of rotations = 360Ï€/(5Ï€) = ...
so the smaller wheel with a circumference of 5Ï€ must cover the same distance
number of rotations = 360Ï€/(5Ï€) = ...
Let's start by calculating the circumference of the larger rear wheel. The formula to calculate the circumference of a circle is C = πd, where C represents the circumference and d represents the diameter.
For the larger wheel with a diameter of 6 inches, the circumference is:
C1 = π * 6 = 18.85 inches (rounded to two decimal places)
Now, we can set up a ratio using the circumference of the larger wheel (C1) as a reference point. The number of revolutions made by the larger wheel (R1) is equal to the number of revolutions made by the smaller wheel (R2) multiplied by the ratio of their circumferences.
C1 / C2 = R1 / R2
Substituting the values we have:
18.85 / C2 = 60 / R2
Now, let's solve for R2, the number of revolutions made by the smaller wheel with a diameter of 5 inches.
We can rewrite the equation as:
R2 = (C2 * 60) / 18.85
We know that the diameter of the smaller wheel is 5 inches, so we can calculate its circumference:
C2 = π * 5 = 15.71 inches (rounded to two decimal places)
Plugging this value into the equation, we have:
R2 = (15.71 * 60) / 18.85
Performing the calculations, we find:
R2 ≈ 50.46
Therefore, the smaller wheel will make approximately 50.46 revolutions if it has a diameter of 5 inches.