AMC12 2019 A

AMC12 2019 A · Q1

AMC12 2019 A · Q1. It mainly tests Percent, Area & perimeter.

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 $N$?

半径为 4 英寸的比萨的面积比半径为 3 英寸的比萨的面积大 $N$ 百分比。最接近 $N$ 的整数是多少？

(A) 25 25

(B) 33 33

(D) 66 66

(E) 78 78

Answer

Correct choice: (E)

正确答案：（E）

Solution

The area of the smaller pizza is $\pi \cdot 3^2 = 9\pi$ in$^2$. The area of the larger pizza is $\pi \cdot 4^2 = 16\pi$ in$^2$. The difference is $7\pi$ in$^2$. Therefore the larger pizza's area is $\frac{7\pi}{9\pi} = \frac{7}{9} = 0.777 \dots \approx 78\%$ larger.

小比萨的面积是 $\pi \cdot 3^2 = 9\pi$ 平方英寸。大比萨的面积是 $\pi \cdot 4^2 = 16\pi$ 平方英寸。差值为 $7\pi$ 平方英寸。因此大比萨的面积比小比萨大 $\frac{7\pi}{9\pi} = \frac{7}{9} = 0.777 \dots \approx 78\%$ 。

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