First, find the circumference of the wheel. The formula is C = [tex]2\pi r[/tex].
The radius is half the diameter. The diameter is 22 inches, so the radius is 11 inches. So the circumference is [tex]2\pi\left(11\right)[/tex]in.
To find the total rotations over a mile, we take the total distance divided by the circumference:
[tex]\frac{66360}{2\pi\left(11\right)}[/tex] = 960.13 or 960.
Answer:
960 times
Step-by-step explanation:
First, let's find the circumference of the bicycle wheel using its diameter:
[tex]\Large\boxed{\boxed{\sf Circumference (C) =\sf \pi \times \textsf{diameter}}} [/tex]
Given that the diameter of the bicycle wheel is 22 inches, we have:
[tex]\sf C = \pi \times 22 [/tex]
[tex]\sf C = 22\pi [/tex]
Now, let's find how many times the wheel would go around (complete rotation) if the rider wanted to ride for 1 mile (66,360 inches):
[tex]\begin{aligned} \textsf{Number of rotations} & = \dfrac{\textsf{Distance}}{\textsf{Circumference}} \\\\ & = \dfrac{66360}{22\pi} \\\\ & = \dfrac{66360}{22\pi} \\\\\ & = \dfrac{66360}{22\cdot 3.141592654} \\\\ & = \dfrac{66360}{ 69.11503838 } \\\\ & = 960.1383658 \\\\ & = 960 \textsf{(in nearest whole number)}\end{aligned}[/tex]
So, the wheel would go around approximately 960 times if the rider wanted to ride for 1 mile.
