Question

question 3 of 40

below is the justification for the formula for area of a circle. which word, when placed in the blank, best completes this argument?

• the circumference of a circle is given by the formula \\(c = 2\pi r\\), where \\(r\\) is the radius.
• if the circle is divided into equally sized sectors, the sectors can be rearranged to form a shape that approximates a parallelogram.
• the base of the parallelogram is _____, and the height is \\(r\\).
• because the area of a parallelogram is equal to the product of the base and the height, the area is \\(\pi r^2\\).
• therefore, the area of a circle is given by the formula \\(\pi r^2\\).

a. half the radius, or \\(\frac{1}{2}r\\)
b. the radius, \\(r\\)
c. half the circumference, or \\(\pi r\\)
d. the circumference, or \\(2\pi r^2\\)

Explanation:

Relate the parallelogram base to the circle's circumference

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Verify the area formula with the height

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Answer:

• A. half the radius, or \(\frac{1}{2}r\)
• B. the radius, \(r\)
• C. half the circumference, or \(\pi r\) (Correct answer)
• D. the circumference, or \(2\pi r^2\)