AMC12 2016 B

AMC12 2016 B · Q8

AMC12 2016 B · Q8. It mainly tests Fractions, 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片，形状为边长为 3 英寸的正三角形，重 12 盎司。第二块同种木材（厚度相同）的薄木片也为正三角形，边长为 5 英寸。下列哪一项最接近第二块木片的重量（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）：密度均匀的物体的重量与其体积成正比。厚度均匀的三角形木片的体积与三角形的面积成正比。第二块木片的边长是第一块的 $\frac{5}{3}$ 倍，因此第二块的面积是第一块的 $\left(\frac{5}{3}\right)^2$ 倍。因此重量为 $12\cdot\left(\frac{5}{3}\right)^2=\frac{100}{3}\approx 33.3$ 盎司。

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