Question

a bicycle wheel is 63 centimeters from top to bottom. when the wheel goes all the way around one time, the bicycle travels 198 centimeters. how can this information be used to estimate the value of π? image of a bicycle wheel with 63 cm labeled click the arrows to choose an answer from each menu. because the wheel is circular, the height of the wheel is the choose... of the circle. the distance traveled by the wheel when it goes all the way around one time is the choose... of the circle. to estimate the value of π, choose... the distance traveled by the wheel when it goes all the way around by choose...

Explanation:

Step1: Identify wheel height as diameter

The height of the wheel (63 cm) is the diameter ($d$) of the circular wheel. So, $d = 63$ cm.

Step2: Identify distance as circumference

The distance traveled in one full rotation (198 cm) is the circumference ($C$) of the circle. The formula for circumference is $C=\pi d$.

Step3: Solve for $\pi$

To find $\pi$, we rearrange the formula: $\pi=\frac{C}{d}$. Substitute $C = 198$ cm and $d = 63$ cm. So, $\pi=\frac{198}{63}$. Simplifying, $\frac{198\div9}{63\div9}=\frac{22}{7}\approx3.14$ (or directly dividing 198 by 63 gives approximately 3.14).

Answer:

The height of the wheel is the diameter of the circle. The distance traveled is the circumference of the circle. To estimate $\pi$, divide the distance traveled (circumference) by the diameter (height of the wheel). Calculation: $\pi\approx\frac{198}{63}\approx3.14$.