2. 外语
  3. The relationship between the area A of a circle and its circumference C is given by the formula A = kC2, where k is a constant.

The relationship between the area A of a circle and its circumference C is given by the formula A = kC2, where k is a constant.

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问题 The relationship between the area A of a circle and its circumference C is given by the formula A = kC2, where k is a constant. What is the value of k ?
选项 A、
B、
C、1/4
D、2π
E、4π2
答案A
解析 One way to approach this problem is to realize that the value of the constant k is the same for all circles. Therefore, you can pick a specific circle and substitute the circumference and the area of that particular circle into the formula and calculate the value of k.
    Say, for example, that you pick a circle with radius 1. The area of the circle is n and the circumference of the circle is 2π. Inserting these values into the formula gives n = k(2π)2. Solving this equation for k gives k=, and the correct answer is Choice A.
    Another way to approach the problem is to express A and C in terms of a common variable and then solve the resulting equation for k. Recall the commonly used formulas for the area and the circumference of a circle: A = πr2 and C = 2πr. Note that in these formulas, both A and C are expressed in terms of the radius r. So, in the formula A = kC2, you can substitute expressions for A and C in terms of r.
    Substituting πr2 for A and 2πr for C gives πr2 = k(2πr)2.
    Now you can determine the value of k by solving the equation for k as follows.

The correct answer is Choice A.
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