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.