Question

estimates of π
example estimate π.
circular object d = diameter c = circumference \\( \frac { c } { d } = \pi \\)
roll of tape 3.5 inches 11 inches \\( \frac { 11 } { 3.5 } = 11 \div 3.5 \\)
\\( \pi \approx 11 \div 3.5 \approx 3.14 \\)
plate 10.5 inches 33 inches \\( \frac { 33 } { 10.5 } = 33 \div 10.5 \\)
\\( \pi \approx 33 \div 10.5 \approx 3.14 \\)
π is about 3.14
directions complete the chart. round \\( \frac { c } { d } \\) to the nearest hundredth.

Explanation:

Tabletop

Step1: Calculate $\frac{C}{d}$

We know that $C = 6.5$ ft and $d=2$ ft. Using the formula $\frac{C}{d}$, we substitute the values: $\frac{6.5}{2}=3.25$

Roll of tape

Step1: Calculate $d$

We know that $C = 17.27$ cm and $\frac{C}{d}=3.14$. Using the formula $d=\frac{C}{\frac{C}{d}}$, we substitute the values: $d=\frac{17.27}{3.14} = 5.5$ cm

CD

Step1: Calculate $C$

We know that $d = 12$ cm and $\frac{C}{d}=3.14$. Using the formula $C=\frac{C}{d}\times d$, we substitute the values: $C=3.14\times12 = 37.68$ cm

Bottle cap

Step1: Calculate $C$

We know that $d = 2.5$ cm and $\frac{C}{d}=3.14$. Using the formula $C=\frac{C}{d}\times d$, we substitute the values: $C=3.14\times2.5=7.85$ cm

Glass base

Step1: Calculate $\frac{C}{d}$

We know that $C = 9.53$ in and $d = 3$ in. Using the formula $\frac{C}{d}$, we substitute the values: $\frac{9.53}{3}\approx3.18$

Answer:

Circular Object	Diameter, \(d=\frac{C}{\pi}\)	Circumference, \(C = \pi d\)	pi, \(\frac{C}{d}=\) estimate of \(\pi\)
roll of tape	\(5.5\) cm	\(17.27\) cm	\(3.14\)
CD	\(12\) cm	\(37.68\) cm	\(3.14\)
bottle cap	\(2.5\) cm	\(7.85\) cm	\(3.14\)
glass base	\(3\) in.	\(9.53\) in.	\(3.18\)