2019 AMC 12A 第 1 题

Question

半径为

4

英寸的披萨面积比半径为

3

英寸的披萨面积大

N

%。最接近

N

的整数是多少？

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

两个面积之比为

4^2 : 3^2

。

The areas are in the ratio

4^2 : 3^2

百分比增幅是

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

The percent increase is

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

圆面积与半径的平方成正比，所以较大面积与较小面积的比为

\dfrac{16}{9}

。

百分比增幅为

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

最接近的整数是

78

。

所以正确答案是 E。

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.

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