Question

2 complete the table. use one of the approximate values for π discussed in class (for example 3.14, \frac{22}{7}, 3.1416). explain or show your reasoning.

Explanation:

Step1: Find the circumference of the hula - hoop

The formula for the circumference of a circle is \(C=\pi d\). Given \(d = 35\) in. Let's use \(\pi=\frac{22}{7}\).

$$C=\frac{22}{7}\times35$$

$$C = 22\times5=110$$

in.

Step2: Find the diameter of the circular pond

Using the formula \(C=\pi d\), we can solve for \(d\). Given \(C = 556\) ft and \(\pi=\frac{22}{7}\). Then \(d=\frac{C}{\pi}\)

$$d=\frac{556}{\frac{22}{7}}=\frac{556\times7}{22}=\frac{3892}{22}\approx176.91$$

ft.

Step3: Find the circumference of the magnifying glass

Using \(C=\pi d\), with \(d = 5.2\) cm and \(\pi = 3.14\)

$$C=3.14\times5.2=16.328$$

cm.

Step4: Find the diameter of the car - tire

Using \(d=\frac{C}{\pi}\), with \(C = 71.6\) in and \(\pi=\frac{22}{7}\)

$$d=\frac{71.6}{\frac{22}{7}}=\frac{71.6\times7}{22}=\frac{501.2}{22}\approx22.78$$

in.

Answer:

object	diameter	circumference
circular pond	\(\approx176.91\) ft	\(556\) ft
magnifying glass	\(5.2\) cm	\(16.328\) cm
car tire	\(\approx22.78\) in	\(71.6\) in