AMC8 2003

AMC8 2003 · Q8

AMC8 2003 · Q8. It mainly tests Arithmetic misc, Area & perimeter.

Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown. Each friend uses the same amount of dough, and Art makes exactly 12 cookies. Who gets the fewest cookies from one batch of cookie dough?

问题 8、9 和 10 使用伴随段落和图中的数据。烘焙义卖四位朋友 Art、Roger、Paul 和 Trisha 烤饼干，所有饼干厚度相同。饼干形状不同，如图所示。谁从一批曲奇面团中分到的曲奇最少？

(A) Art Art

(B) Paul Paul

(D) Trisha Trisha

(E) There is a tie for fewest. 并列最少。

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Because all of the cookies have the same thickness, only the surface area of their shapes needs to be considered. The surface area of each of Art’s trapezoid cookies is $\frac{1}{2}\cdot 3\cdot 8=12\ \text{in}^2$. Since he makes 12 cookies, the surface area of the dough is $12\times 12=144\ \text{in}^2$. Roger’s rectangle cookies each have surface area $2\cdot 4=8\ \text{in}^2$; therefore, he makes $144\div 8=18$ cookies. Paul’s parallelogram cookies each have surface area $2\cdot 3=6\ \text{in}^2$. He makes $144\div 6=24$ cookies. Trisha’s triangle cookies each have surface area $\frac{1}{2}\cdot 4\cdot 3=6\ \text{in}^2$. She makes $144\div 6=24$ cookies. So Art makes the fewest cookies.

（A）因为所有饼干的厚度相同，所以只需要考虑它们形状的表面积。Art 的每块梯形饼干的表面积为 $\frac{1}{2}\cdot 3\cdot 8=12\ \text{in}^2$。由于他做了 12 块饼干，因此面团的表面积为 $12\times 12=144\ \text{in}^2$。 Roger 的每块长方形饼干的表面积为 $2\cdot 4=8\ \text{in}^2$；因此，他能做 $144\div 8=18$ 块饼干。 Paul 的每块平行四边形饼干的表面积为 $2\cdot 3=6\ \text{in}^2$。他能做 $144\div 6=24$ 块饼干。 Trisha 的每块三角形饼干的表面积为 $\frac{1}{2}\cdot 4\cdot 3=6\ \text{in}^2$。她能做 $144\div 6=24$ 块饼干。所以 Art 做的饼干最少。

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