If a wheel has a radius of 3 in how far will it travel in 30 revolutions?

ANSWER:

180π units

The distance the wheel will travel in 30 revolutions is 180π units.

STEP-BY-STEP EXPLANATION:

The shape of a wheel is circular.

To find the distance the wheel will travel for 30 revolutions, we must first find the distance it will travel for 1 revolution.

1 revolution of the wheel would be equivalent to the circumference of the wheel as it is a circle.

Therefore, we will require the formula for the circumference of a circle in order to solve this question.

The formula for the circumference of a circle is displayed below:

Let C = circumference of circle

C = 2πr OR C = πd

Where r = radius of circle

Where d = diameter of circle

Using this, we will substitute the given value from the problem into the formula to obtain the distance the wheel will travel for 1 revolution.

Let d = distance the wheel will travel for 1 revolution

r = 3 units

d = 2πr

THEREFORE:

d = 2π( 3 )

d = 6π units

In order to obtain the distance the wheel will travel for 30 revolutions, we simply have to multiply the distance the wheel will travel for 1 revolution ( as given above ) by 30.

Let x = distance the wheel will travel for 30 revolutions

x = d × 30

x = 6π × 30

x = 180π units