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? 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's height as diameter

The height from top to bottom of the circular wheel is its diameter (\(d = 63\) cm).

Step2: Identify distance as circumference

The distance traveled in one full rotation is the circumference (\(C = 198\) cm).

Step3: Recall circumference formula

The formula for the circumference of a circle is \(C=\pi d\).

Step4: Solve for \(\pi\)

To find \(\pi\), we rearrange the formula: \(\pi=\frac{C}{d}\). Substitute \(C = 198\) and \(d = 63\): \(\pi=\frac{198}{63}\approx3.14\) (simplifying the fraction or dividing gives the approximation for \(\pi\)).

Answer:

Because the wheel is circular, the height of the wheel is the \(\boldsymbol{\text{diameter}}\) of the circle. The distance traveled by the wheel when it goes all the way around one time is the \(\boldsymbol{\text{circumference}}\) of the circle. To estimate the value of \(\pi\), \(\boldsymbol{\text{divide}}\) the distance traveled by the wheel when it goes all the way around by \(\boldsymbol{\text{the diameter of the wheel}}\). Calculating \(\frac{198}{63}\approx3.14\) gives an estimate for \(\pi\).