2000 AMC 8 Problem 19
Attempt Problem 19 of the 2000 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 2000 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Three circular arcs of radius units bound the region shown. Arcs and are quarter-circles, and arc is a semicircle. What is the area, in square units, of the region?
Answer: C
Small hint:
Move the curved pieces to make a rectangle
Big hint:
The rearranged rectangle has dimensions and
Solution:
Create a rectangle that covers the bottom half of the figure as shown below.
Then, we get that
We also know that
and are both quarter-circles that form a semicircle with the same area as
This means that and
Thus, C is the correct answer.
Problem 19 in other years
- 1985 AMC 8
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