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