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?
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because the wheel is circular, the height of the wheel is the
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of the circle. the distance traveled by the wheel when it goes all the way around one time is the
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the distance
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of the circle. to estimate the value of π,

Explanation:

Step1: Identify diameter and circumference

Diameter $d = 63$ cm, Circumference $C = 198$ cm

Step2: Recall circumference formula

$C = \pi d$

Step3: Solve for $\pi$

Rearrange formula: $\pi = \frac{C}{d}$
Substitute values: $\pi = \frac{198}{63}$
Simplify the fraction: $\frac{198\div9}{63\div9} = \frac{22}{7}$

Answer:

First, recognize that the 63 cm is the diameter of the circle, and the 198 cm distance traveled is the circumference of the circle. Then use the circumference formula $C=\pi d$, rearrange to $\pi=\frac{C}{d}$, substitute the values: $\pi=\frac{198}{63}=\frac{22}{7}\approx3.14$.

To fill the blanks:

• Because the wheel is circular, the height of the wheel is the diameter of the circle.
• The distance traveled by the wheel when it goes all the way around one time is the circumference of the circle.
• To estimate the value of $\pi$, divide the circumference by the diameter (calculate $\frac{198}{63}$).

The estimated value of $\pi$ is $\frac{22}{7}$ (or approximately 3.14).