Answer :
Answer:
The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.
Pi = π = 3.14
Step-by-step explanation:
Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)
The formula for the circumference of circle when Diameter is given = πD
π = Circumference / Diameter
For Circle A :
Circle A has a diameter of 7 inches, a circumference of 21.98 inches.
π = 21.98 inches/7 inches
π = 3.14
For Circle B
The diameter of circle B is 6 inches, the circumference is 18.84 inches
π = 18.84 inches/6 inches
π = 3.14
Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)
The formula for the area of the circle = πr²
Circle A has a diameter of 7 inches, an area of 38.465 square inches.
r = Radius = 7 inches ÷ 2
= 3.5 inches
π = Area / Radius²
π = 38.465 in²/(3.5 inches)²
π = 3.14
For Circle B
The diameter of circle B is 6 inches, and the area is 28.26 square inches.
r = Radius = 6 inches ÷ 2
= 3 inches
π = Area / Radius²
π = 28.26 in²/(3 inches)²
π = 3.14
Part C: What observation can you make about the value of pi for circles A and B? (2 points)
The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.
The observation is that the values of [tex]\pi[/tex] remain 3.14 when [tex]\pi[/tex] is calculated from the areas and circumferences of both circles
The circumference of a circle
The given parameters are:
Circle A
- Diameter = 7 inches
- Circumference = 21.98 inches
Circle B
- Diameter = 6 inches
- Circumference = 18.84 inches
The circumference of a circle is:
[tex]C= \pi d[/tex]
Make [tex]\pi[/tex] the subject
[tex]\pi = \frac{C}{d}[/tex]
For circle A, we have:
[tex]\pi_A = \frac{21.98}{7}[/tex]
[tex]\pi_A = 3.14[/tex]
For circle B, we have:
[tex]\pi_B = \frac{18.84}{6}[/tex]
[tex]\pi_B = 3.14[/tex]
Hence, the value of [tex]\pi[/tex] in both circles is 3.14
The area of a circle
The given parameters are:
Circle A
- Diameter = 7 inches
- Area = 38.465 square inches.
Circle B
- Diameter = 6 inches
- Area = 28.26 square inches
The area of a circle is:
[tex]A= \pi \frac{d^2}{4}[/tex]
Make [tex]\pi[/tex] the subject
[tex]\pi = \frac{4A}{d^2}[/tex]
For circle A, we have:
[tex]\pi_A = \frac{4 * 38.465 }{7^2}[/tex]
[tex]\pi_A = 3.14[/tex]
For circle B, we have:
[tex]\pi_B = \frac{4 * 28.26 }{6^2}[/tex]
[tex]\pi_B = 3.14[/tex]
Hence, the value of [tex]\pi[/tex] in both circles is 3.14
The value of pi
The observation is that the values of [tex]\pi[/tex] in both circles when area and circumference are used is 3.14
Read more about area and circumference at:
https://brainly.com/question/15673093