Question

Circle A has a diameter of 8 inches, a circumference of 25.12 inches, and an area of 50.24 square inches. The diameter of circle B is 3 inches, the circumference is 9.42 inches, and the area is 7.065 square inches.
Part A: Using the formula for circumference, solve for the value of pi for each circle.
Part B: Use the formula for area and solve for the value of pi for each circle.

Part C: What observation can you make about the value of pi for circles A and B?

Answer 1

This is the formula for circumference:
$C =$π$d$

Substituting the values from circle A, we get this:
25.12 = 8π
π = $\frac{25.12}{8}$
π = 3.14
 
Using the values from circle B, we get this:
9.42 = 3π
π = $\frac{9.42}{3}$
π = 3.14

The formula for area is:
$A =$π$r^{2}$

Using the values from circle A, we get this (also using $r = \frac{d}{2}$):
50.24 = π $* (\frac{8}{2})^{2}$
50.24 = π $* (4)^{2}$
50.24 = 16π
π = $\frac{50.24}{16}$
π = 3.14

Using the values from circle B, we get this:
7.065 = π $* (\frac{3}{2})^{2}$
7.065 = π $* \frac{9}{4}$
7.065 = $\frac{9}{4}$π
π = $\frac{7.064}{\frac{9}{4}}$
π = 3.14

The observation is that π = 3.14, although in reality this is only an approximation to 3 significant figures, since π is a transcendental number.

I hope this helps you