AMC10 2016 B

AMC10 2016 B · Q10

AMC10 2016 B · Q10. It mainly tests Ratios & proportions, Area & perimeter.

A thin piece of wood of uniform density in the shape of an equilateral triangle with side length 3 inches weighs 12 ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side length 5 inches. Which of the following is closest to the weight, in ounces, of the second piece?

一块密度均匀的薄木板，形状为边长为 3 英寸的等边三角形，重量为 12 盎司。另一块同种木材且厚度相同的薄木板，同样为等边三角形，边长为 5 英寸。下列选项中，哪一个最接近第二块木板的重量（单位：盎司）？

(A) 14.0 14.0

(B) 16.0 16.0

(D) 33.3 33.3

(E) 55.6 55.6

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The weight of an object of uniform density is proportional to its volume. The volume of the triangular piece of wood of uniform thickness is proportional to the area of the triangle. The side length of the second piece is $\frac{5}{3}$ times the side length of the first piece, so the area of the second piece is $\left(\frac{5}{3}\right)^2$ times the area of the first piece. Therefore the weight is $12\cdot\left(\frac{5}{3}\right)^2=\frac{100}{3}\approx 33.3$ ounces.

答案（D）：均匀密度物体的重量与其体积成正比。厚度均匀的三角形木块的体积与该三角形的面积成正比。第二块的边长是第一块边长的 $\frac{5}{3}$ 倍，因此第二块的面积是第一块面积的 $\left(\frac{5}{3}\right)^2$ 倍。所以重量为 $12\cdot\left(\frac{5}{3}\right)^2=\frac{100}{3}\approx 33.3$ 盎司。

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