A bicycle has smaller front wheel and larger rear wheel.if the rear wheel has diameter 6 inches and it does 60 revolution, how many revolution will the smaller wheel makes if it has diameter of 5 inches?

6in/5in * 60rev = 72 revs.

distance covered by the larger wheel = 60(6π) = 360π inches

so the smaller wheel with a circumference of 5π must cover the same distance
number of rotations = 360π/(5π) = ...

To find out how many revolutions the smaller wheel will make, we can use the concept of ratios and proportions.

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.