A wheel with a radius of 13 rolls along level ground and makes 4 1/2 revolutions per second. Assuming the circumference to be 3.1416 times the diameter, how far does the wheel travel in 8 seconds?

distance= circumference*number rotations

= 3.1416*(2*13)*4.5*8

3.1416*(2*13)*4.5*8

To find how far the wheel travels in 8 seconds, we need to calculate the distance covered in one revolution and multiply it by the number of revolutions made in 8 seconds.

First, let's find the circumference of the wheel. We are given that the circumference is 3.1416 times the diameter. The diameter of the wheel is twice the radius, so:

Diameter = 2 * Radius = 2 * 13 = 26 units

Now we can calculate the circumference of the wheel:

Circumference = π * Diameter = 3.1416 * 26 ≈ 81.68 units

Next, let's find the distance covered in one revolution by using the circumference formula: Distance = Circumference.

Distance covered in one revolution = 81.68 units

Since the wheel makes 4 1/2 revolutions per second, we need to calculate the distance covered in one second:

Distance covered in one second = 4.5 * Distance covered in one revolution

Distance covered in one second = 4.5 * 81.68 ≈ 367.56 units

Finally, to find the distance covered in 8 seconds, we multiply the distance covered in one second by 8:

Distance covered in 8 seconds = Distance covered in one second * 8

Distance covered in 8 seconds = 367.56 * 8 ≈ 2940.48 units

Therefore, the wheel travels approximately 2940.48 units in 8 seconds.