Question

date:
describe π as ratio of \\(\frac{c}{d}\\)
skills practice
directions: complete the table below using the provided information. then, answer the following questions.

circle\tradius\tdiameter\tcircumference\tratio of \\(\frac{c}{d}\\)
a\t5\t10\t31.4\t\\(\frac{c}{d}=\frac{31.4}{10}=3.14\\)
b\t\t8\t25.12\t
c\t\t16\t50.24\t
d\t2\t\t12.56\t
e\t6\t\t37.68\t

1. what is a ratio? in the last column on the far right, what are the two things we are comparing?

1. what do you notice about the ratio of circumference to its diameter for all circles?

Explanation:

For Circle B:

Step 1: Find Radius

The radius \( r \) is half of the diameter \( d \). Given \( d = 8 \), so \( r=\frac{d}{2}=\frac{8}{2} = 4 \).

Step 2: Find Ratio \( \frac{C}{D} \)

Using the formula \( \frac{C}{D}=\frac{25.12}{8}=3.14 \).

For Circle C:

Step 1: Find Radius

Given \( d = 16 \), so \( r=\frac{d}{2}=\frac{16}{2}=8 \).

Step 2: Find Ratio \( \frac{C}{D} \)

Using the formula \( \frac{C}{D}=\frac{50.24}{16}=3.14 \).

For Circle D:

Step 1: Find Diameter

The diameter \( d = 2r \). Given \( r = 2 \), so \( d=2\times2 = 4 \).

Step 2: Find Ratio \( \frac{C}{D} \)

Using the formula \( \frac{C}{D}=\frac{12.56}{4}=3.14 \).

For Circle E:

Step 1: Find Diameter

The diameter \( d = 2r \). Given \( r = 6 \), so \( d=2\times6=12 \).

Step 2: Find Ratio \( \frac{C}{D} \)

Using the formula \( \frac{C}{D}=\frac{37.68}{12}=3.14 \).

Filling the table:

CIRCLE	RADIUS	DIAMETER	CIRCUMFERENCE	RATIO OF \( \frac{C}{D} \)
B	4	8	25.12	\( \frac{25.12}{8}=3.14 \)
C	8	16	50.24	\( \frac{50.24}{16}=3.14 \)
D	2	4	12.56	\( \frac{12.56}{4}=3.14 \)
E	6	12	37.68	\( \frac{37.68}{12}=3.14 \)

Answer:

ing the questions:

1.

• A ratio is a comparison of two quantities by division. In the last column, we are comparing the circumference (\( C \)) of the circle to its diameter (\( D \)).

2.

The ratio of the circumference to the diameter (\( \frac{C}{D} \)) is approximately \( 3.14 \) (which is the value of \( \pi \)) for all circles. This shows that the ratio of the circumference of a circle to its diameter is a constant ( \( \pi \) ), regardless of the size of the circle.