Question

Question 3 (Essay Worth 10 points)

(05.04 MC)
Circle A has a diameter of 9 inches, a circumference of 28.26 inches, and an area of 63.585 square inches. The diameter of circle B is 5 inches, the circumference is 15.70
inches, and the area is 19.625 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

Explanation:

area of a circle

A = pi × r²

circumference of a circle

C = 2 × pi × r

r = diameter / 2 (the radius is half of the diameter)

circle A

A = 63.585 = pi × 4.5² = pi × 20.25

pi = 63.585 / 20.25 = 3.14

C = 28.26 = 2 × pi × 4.5

pi = 28.26 / (2 × 4.5) = 28.26 / 9 = 3.14

circle B

A = 19.625 = pi × 2.5² = pi × 6.25

pi = 19.625 / 6.25 = 3.14

C = 15.7 = 2 × pi × 2.5

pi = 15.7 / (2 × 2.5) = 15.7 / 5 = 3.14

pi is always the same for every circle of any size. it is a natural constant defining the circumference and area of every circle in relation to the actual radius or diameter.