2019 AMC 12A Problem 1

Attempt Problem 1 of the 2019 AMC 12A 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 2019 AMC 12A solutions, or check the answer key.

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

The area of a pizza with radius

4

inches is

N

percent larger than the area of a pizza with radius

3

inches. What is the integer closest to

N?

25

33

44

66

78

The areas are in the ratio

4^2 : 3^2

The percent increase is

\left(\dfrac{16}{9} - 1\right) \times 100

The areas are proportional to the squares of the radii, so the ratio of the larger area to the smaller is

\dfrac{16}{9}.

The percent increase is

\left(\dfrac{16}{9} - 1\right) \times 100 = \dfrac{700}{9} \approx 77.8.

The closest integer is

78.

Thus, the correct answer is E.

Problem 1 in other years