Question

如图摆放时，六片圆形意大利辣香肠正好横跨一个 $12$ 英寸披萨的直径。如果总共 $24$ 片辣香肠无重叠地放在这个披萨上，披萨面积的几分之几被辣香肠覆盖？

Six pepperoni circles will exactly fit across the diameter of a $12$ -inch pizza when placed as shown. If a total of $24$ circles of pepperoni are placed on this pizza without overlap, what fraction of the pizza is covered by pepperoni?

$\ \dfrac 12$

$\ \dfrac 23$

$\ \dfrac 34$

$\ \dfrac 56$

$\ \dfrac 78$

答案：B

知识点：圆面积面积比长度、面积与体积的缩放关系

难度评级：1030

解答：

每片圆形辣香肠的直径是大圆直径的 $\dfrac{1}{6}$ ，所以它的面积是总面积的 $(\frac 16)^2 = \frac 1{36}$ 。

因为有 $24$ 片辣香肠，所以覆盖面积为 $24 \cdot \dfrac 1{36} = \frac 23$ 。

所以正确答案是 B。

Each circle has $\dfrac{1}{6}$ the diameter of the large circle, so it has $(\frac 16)^2 = \frac 1{36}$ of the total area.

Since there are $24$ pepperoni, they take up $24 \cdot \dfrac 1{36} = \frac 23$ of the area.

Therefore, the answer is B .

2010 AMC 8 第 10 题

答案：B

难度评级：1030

解答：

其他年份的第 10 题