Question

part a
complete the table. use one of the approximate values for π discussed in class (for example 3.14, 22/7, 3.1416) and round to the nearest whole number.

hula hoop: diameter = 35 in, circumference = blank in

circular pond: diameter = blank ft, circumference = 556 ft

magnifying glass: diameter = 5.2 cm, circumference = blank cm

car tire: diameter = blank in, circumference = 71.6 in

Explanation:

Step1: Calculate the circumference of the Hula Hoop

The formula for the circumference of a circle is \(C = \pi d\). Given \(d = 35\) in and using \(\pi=\frac{22}{7}\).
\(C=\frac{22}{7}\times35\)
\(C = 22\times5=110\) in

Step2: Calculate the diameter of the Circular Pond

Using the formula \(C=\pi d\), we can solve for \(d\). Given \(C = 556\) ft and \(\pi=\frac{22}{7}\).
\(d=\frac{C}{\pi}=\frac{556}{\frac{22}{7}}=\frac{556\times7}{22}=\frac{3892}{22}\approx177\) ft

Step3: Calculate the circumference of the Magnifying Glass

Using \(C=\pi d\), with \(d = 5.2\) cm and \(\pi = 3.14\).
\(C=3.14\times5.2=16.328\approx16\) cm

Step4: Calculate the diameter of the Car Tire

Using \(d=\frac{C}{\pi}\), with \(C = 71.6\) in and \(\pi=\frac{22}{7}\).
\(d=\frac{71.6}{\frac{22}{7}}=\frac{71.6\times7}{22}=\frac{501.2}{22}\approx23\) in

Answer:

Object	Diameter	Circumference
Circular Pond	\(177\) ft	\(556\) ft
Magnifying Glass	\(5.2\) cm	\(16\) cm
Car Tire	\(23\) in	\(71.6\) in