Question

c. use the given information to complete the table. use 3.14 for π. then verify that π is the ratio of the circumference to the diameter for each circle. 1. circle 1: ( d = 4 , \text{cm} ) 2. circle 2: ( r = 7 , \text{mm} ) 3. circle 3: ( r = 12 , \text{in} ) 4. circle 4: ( d = 10 , \text{mm} ) 5. circle 5: ( r = 2.5 , \text{m} ) 6. circle 6: ( d = 7 , \text{in} )

	circle	circumference	radius	diameter	( pi = \text{circumference} / \text{diameter} )
1.	circle 1
2.	circle 2
3.	circle 3
4.	circle 4
5.	circle 5
6.	circle 6

Explanation:

Step1: Recall circle formulas

Radius $r = \frac{d}{2}$, Diameter $d = 2r$, Circumference $C = \pi d = 2\pi r$, Ratio $\frac{C}{d} = \pi$

Step2: Solve for Circle 1

Given $d=4$ cm.
$r = \frac{4}{2} = 2$ cm
$C = 3.14 \times 4 = 12.56$ cm
$\frac{C}{d} = \frac{12.56}{4} = 3.14$

Step3: Solve for Circle 2

Given $r=7$ mm.
$d = 2 \times 7 = 14$ mm
$C = 2 \times 3.14 \times 7 = 43.96$ mm
$\frac{C}{d} = \frac{43.96}{14} = 3.14$

Step4: Solve for Circle 3

Given $r=12$ in.
$d = 2 \times 12 = 24$ in
$C = 2 \times 3.14 \times 12 = 75.36$ in
$\frac{C}{d} = \frac{75.36}{24} = 3.14$

Step5: Solve for Circle 4

Given $d=10$ mm.
$r = \frac{10}{2} = 5$ mm
$C = 3.14 \times 10 = 31.4$ mm
$\frac{C}{d} = \frac{31.4}{10} = 3.14$

Step6: Solve for Circle 5

Given $r=2.5$ m.
$d = 2 \times 2.5 = 5$ m
$C = 2 \times 3.14 \times 2.5 = 15.7$ m
$\frac{C}{d} = \frac{15.7}{5} = 3.14$

Step7: Solve for Circle 6

Given $d=7$ in.
$r = \frac{7}{2} = 3.5$ in
$C = 3.14 \times 7 = 21.98$ in
$\frac{C}{d} = \frac{21.98}{7} = 3.14$

Answer:

Circle	Circumference	Radius	Diameter	$\pi =$ Circumference/ Diameter
2. Circle 2	43.96 mm	7 mm	14 mm	3.14
3. Circle 3	75.36 in	12 in	24 in	3.14
4. Circle 4	31.4 mm	5 mm	10 mm	3.14
5. Circle 5	15.7 m	2.5 m	5 m	3.14
6. Circle 6	21.98 in	3.5 in	7 in	3.14