Circle A has a diameter of 7 inches, a circumference of 21.98 inches, and an area of 38.465 square inches. The diameter of circle B is 6 inches, the circumference is 18.84 inches, and the area is 28.26 square inches.
Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)
Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)
Part C: What observation can you make about the value of pi for circles A and B?
d = 7
pi * 7 = 21.98
pi = 3.14
pi * 49/4 = 38.465
pi = 3.14 remarkable
d = 6
pi *6 = 18.84
pi = 3.14 even more remarkable
pi * 9 = 28.26
pi = 3.14
Well , Archimedes kept getting the same answer too.
where did the 49/4 come from?
It came from dividing 38.465 by 3.14
Part A:
To solve for the value of π using the formula for circumference, we can rearrange the formula:
C = π * d
Where C is the circumference and d is the diameter.
For Circle A:
C = 21.98 inches, d = 7 inches
Substituting these values into the formula:
21.98 = π * 7
To solve for π, we can rearrange the equation:
π = 21.98 / 7
Calculating the value gives us:
π ≈ 3.14
So, for Circle A, the value of π is approximately 3.14.
For Circle B:
C = 18.84 inches, d = 6 inches
Using the same process as above:
18.84 = π * 6
Rearranging the equation:
π = 18.84 / 6
Calculating the value gives us:
π ≈ 3.14
Therefore, for Circle B, the value of π is also approximately 3.14.
Part B:
To solve for the value of π using the formula for area, we can rearrange the formula:
A = π * r^2
Where A is the area and r is the radius.
For Circle A:
A = 38.465 square inches
To find the radius, we can use the formula:
r = d / 2 = 7 / 2 = 3.5 inches
Now, substituting the values into the formula for area:
38.465 = π * (3.5)^2
To solve for π, we rearrange the equation:
π = 38.465 / (3.5)^2
Calculating the value gives us:
π ≈ 3.14
So, for Circle A, the value of π is approximately 3.14.
For Circle B:
A = 28.26 square inches
Finding the radius:
r = d / 2 = 6 / 2 = 3 inches
Substituting the values into the formula:
28.26 = π * (3)^2
Again, rearranging the equation:
π = 28.26 / (3)^2
Calculating the value gives us:
π ≈ 3.14
Therefore, for Circle B, the value of π is also approximately 3.14.
Part C:
From both Part A and Part B, we observed that the value of π for Circle A and Circle B is approximately 3.14. This value is commonly known as "pi," which is a mathematical constant representing the ratio of a circle's circumference to its diameter. Additionally, regardless of the circle's size or dimensions, the value of π remains constant.