AMC8 2010

AMC8 2010 · Q10

AMC8 2010 · Q10. It mainly tests Area & perimeter.

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?

六个意大利辣香肠圆片正好能如图所示放置在12英寸比萨的直径上。如果总共放置24个不重叠的辣香肠圆片，比萨被辣香肠覆盖的分数是多少？

(A) 1/2 1/2

(B) 2/3 2/3

(D) 5/6 5/6

(E) 7/8 7/8

Answer

Correct choice: (B)

正确答案：（B）

Solution

The pepperoni circles' diameter is $2$, since $\dfrac{12}{6} = 2$. From that we see that the area of the $24$ circles of pepperoni is $\left ( \frac{2}{2} \right )^2 (24\pi) = 24\pi$. The large pizza's area is $6^2\pi$. Therefore, the ratio is $\frac{24\pi}{36\pi} = \boxed{\textbf{(B) }\frac{2}{3}}$

辣香肠圆片的直径是 $2$，因为 $\dfrac{12}{6} = 2$。由此，24个辣香肠圆片的面积是 $\left ( \frac{2}{2} \right )^2 (24\pi) = 24\pi$。大比萨的面积是 $6^2\pi$。因此，比率是 $\frac{24\pi}{36\pi} = \boxed{\textbf{(B) }\frac{2}{3}}$

Topics

GE.007 Area & perimeter