1950 AMC 12 Problem 34

Attempt Problem 34 of the 1950 AMC 12 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 1950 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

34.

When the circumference of a toy balloon is increased from 2020 inches to 2525 inches, the radius is increased by:
55 in
2122\dfrac12 in
5π\dfrac5\pi in
52π\dfrac{5}{2\pi} in
π5\dfrac{\pi}{5} in
Answer: D
Concepts:circumferencealgebraic manipulation
Small hint:
Use C=2πrC=2\pi r for each circumference
Big hint:
The change in circumference is 2π2\pi times the change in radius
Solution:
Because C=2πr,C=2\pi r, the changes satisfy 25−20=2π(rnew−rold). 25-20=2\pi\mathopen{}\left(r_{\mathrm{new}}-r_{\mathrm{old}}\right)\mathclose{}. Hence the radius increases by 52π\dfrac{5}{2\pi} inches.
Thus, the correct answer is D.
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