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. (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? (2 points).

Answer 1

Pi (π) is a transcendental number in mathematics. The value of pi using circumference and area of circle for each specified circle are deduced as:

• Using circumference, for circle A:  π = 3.14, for circle B: π = 3.14
• Using Area formula, for circle A: π = 3.14 , for circle B:π = 3.14

What is the area and circumference of a circle?

Supposing that a considered circle has its radius of 'r' units.

Then, its area and circumference is given as:

• $Area = \pi r^2 \: \rm unit^2$
• $Circumference = 2 \pi r \: \rm units$

Radius of a circle is half of its diameter.

For the given case, finding the value of pi from each of these formulas for each of the specified circle will give us:

Case 1: From circumference formula:

• For circle A:  Its diameter = 8 inches, thus radius = 8/2 = 4 inches

Its circumference is given as 25.12 inches

$25.12 = 2 \times \pi \times (4) = 8\pi\\\text{Dividing both sides by 8}\\\\\pi = \dfrac{25.12}{8} = 3.14$

• For circle B:

Its circumference is given as 9.42 inches

$9.42= 2 \times \pi \times (1.5) = 3\pi\\\text{Dividing both sides by 3}\\\\\pi = \dfrac{9.42}{3} = 3.14$

Case 2: From area formula:

• For circle A: Radius = 4 units and area given is 50.24 sq. inches,

$50.24 = \pi (4)^2 = 16\pi\\\text{Dividing both the sides by 16}\\\\\pi = \dfrac{50.24}{16} = 3.14$

• For circle B: Radius = 1.5 units and area given is 7.065 sq. inches,

$7.065 = \pi (1.5)^2 = 2.25\pi\\\text{Dividing both the sides by 2.25}\\\\\pi = \dfrac{7.065}{2.25} = 3.14$

In reality, π = 3.1415946535... (unending sequence continues)

Hence, The value of pi using circumference and area of circle for each specified circle are deduced as:

• Using circumference, for circle A:  π = 3.14, for circle B: π = 3.14
• Using Area formula, for circle A: π = 3.14 , for circle B:π = 3.14

Learn more about value of pi here:

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