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.

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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
Difficulty rating: 1310
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 2520=2π(rnewrold). 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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