Question

Consider a circle whose size can vary. The circumference of the circle is always 2π times as large as its radius. Let r represent the radius of the circle (in cm) and let C represent the circumference of the circle (in cm). What is the approximate value (rounded to 2 decimal places) of 2π? Write a formula that expresses C in terms of r. As the radius of a circle, r, increases from 2 cm to 7 cm, the circumference of the circle increases from __ to __. A circle's circumference is __ times as large as the circle's diameter, d. What is the relative size of (how many times as large) a circle's' circumference C to its diameter, d? Write an equation to determine the radius of a circle, r, that has a circumference of 19 cm.

Answer 1

The value of 2π is approximately 6.28. The radius r of a circle is directly proportional to its circumference C, with C = 2πr. The radius can be calculated from the circumference using r = C / (2π).

Step-by-step explanation:

The approximate value of 2π rounded to two decimal places is 6.28. This is because π (pi) is approximately 3.14159, so when multiplied by 2, it equals 6.28318, which rounds to 6.28.

The formula that expresses C (the circumference of a circle in cm) in terms of r (the radius in cm) is:

C = 2πr

As the radius of a circle increases from 2 cm to 7 cm, the circumference of the circle increases from 4π cm to 14π cm. For a circle's circumference, we say it is π times as large as the circle's diameter, d. This means the relative size of a circle's circumference C to its diameter d is π:1.

The equation to determine the radius r of a circle that has a circumference of 19 cm is:

r = C / (2π) = 19 cm / (2π) ≈ 3.02 cm