Consider using a circle's radius as the unit for measuring its circle's circumference.

Question

Consider using a circle's radius as the unit for measuring its circle's circumference.

1. If you were to measure any circle's circumference, C, using its radius, r, as the unit of measure, the measurement would be  .   
2. As the circle's radius and circumference vary together the circle's circumference C is always  times as large as the circle's radius, r.
3. Determine if the following statement is true or false:
4.      Since a circle's circumference C is proportional to its radius r, it follows that C is changing at a constant rate of change with r.
5. For any change in a circle's radius, Δr, the circle' circumference changes by      .
6. Since a circle's diameter is 2 times as long as its radius, we can also define a circle's circumference in terms of its diameter, d, by writing, C= .   
7. Think about the meaning of the formula for circumference in terms of diameter you wrote above.
8. The circumference, C, of any circle is always  times as large as its diameter, d
9. If we measure a circle's circumference using its diameter as the unit of measurement, the answer will always be:    
10.      Since Cd=π, we know that π (or about 3.14) is the constant that represents the relative size, or how many times as large, a circle's circumference is compared to its diameter.

Answer 1

1 C(r) = 2pi(r)

2 The circumference is always 2pi time the radius, if you have a perfect circle

4 The derivative of the circumference is its rate of change = C'(r) = 2pi which is a constant. the rate of change is constant.

5 If the radius changes by delta r, then the circumference changes by delta r times 2pi

6 C(d) =pi(d)

7 The circumference is always pi times the diameter

C=pi(d) or C/d = pi = about 3.14159