A rope goes over a circular pulley with a radius of 6.3 cm. If the pulley makes four revolutions without the rope slipping, what length of rope passes over the pulley?

how can i find distance if the only variable given is radius and revolutions?

Arc length = radius * angle (in radians)

In this case, arc length equals length of rope, so

L = r*θ = 6.3*4(2π)

Can you take it from here?

To find the length of the rope passing over the pulley, you can use the formula:

Length of the rope = circumference of the pulley x number of revolutions

The circumference of a circle is calculated with the formula:

Circumference = 2 x π x radius

In this case, the radius of the pulley is given as 6.3 cm. The number of revolutions is given as four.

First, let's calculate the circumference of the pulley:

Circumference = 2 x 3.14 x 6.3 cm
Circumference ≈ 39.48 cm

Next, we can calculate the length of the rope:

Length of the rope = 39.48 cm x 4 (revolutions)
Length of the rope = 157.92 cm

Therefore, the length of the rope passing over the pulley is approximately 157.92 cm.

To find the length of rope that passes over the pulley, you need to calculate the circumference of the pulley's circular path. The formula for calculating the circumference of a circle is C = 2 * π * r, where C is the circumference, π is a mathematical constant approximately equal to 3.14159, and r is the radius.

In this case, the radius of the pulley is given as 6.3 cm. Now, since the pulley makes four complete revolutions, you need to multiply the circumference by the number of revolutions (4) to find the total length of rope that passes over the pulley.

Using the formula C = 2 * π * r, substitute the given radius into the equation:
C = 2 * 3.14159 * 6.3 cm
C ≈ 39.48 cm

Finally, multiply the circumference by the number of revolutions:
Length of rope = 39.48 cm * 4 = 157.92 cm

So, the length of rope that passes over the pulley is approximately 157.92 cm.