Respuesta :
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:
- [tex]Area = \pi r^2 \: \rm unit^2\\[/tex]
- [tex]Circumference = 2 \pi r \: \rm units[/tex]
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
[tex]25.12 = 2 \times \pi \times (4) = 8\pi\\\text{Dividing both sides by 8}\\\\\pi = \dfrac{25.12}{8} = 3.14[/tex]
- For circle B:
Its circumference is given as 9.42 inches
[tex]9.42= 2 \times \pi \times (1.5) = 3\pi\\\text{Dividing both sides by 3}\\\\\pi = \dfrac{9.42}{3} = 3.14[/tex]
Case 2: From area formula:
- For circle A: Radius = 4 units and area given is 50.24 sq. inches,
[tex]50.24 = \pi (4)^2 = 16\pi\\\text{Dividing both the sides by 16}\\\\\pi = \dfrac{50.24}{16} = 3.14[/tex]
- For circle B: Radius = 1.5 units and area given is 7.065 sq. inches,
[tex]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[/tex]
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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