2007 AMC 8 Problem 16
Attempt Problem 16 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
Amanda Reckonwith draws five circles with radii and Then for each circle she plots the point where is its circumference and is its area. Which of the following could be her graph?
Answer: A
Small hint:
Write circumference and area in terms of the radius.
Big hint:
As the circumference grows linearly with radius, the area grows quadratically.
Solution:
The circumferences of circles with radii through are and . Their respective areas are and .
As increases by equal amounts, increases more and more quickly, so the points form an increasing quadratic pattern. Only graph A has that shape.
Thus, A is the correct answer.
Problem 16 in other years
- 1985 AMC 8
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