AMC8 2008

AMC8 2008 · Q16

AMC8 2008 · Q16. It mainly tests 3D geometry (volume), 3D geometry (surface area).

A shape is created by joining seven unit cubes, as shown. What is the ratio of the volume in cubic units to the surface area in square units?

通过连接七个单位立方体形成的形状，如图所示。体积（立方单位）与表面积（平方单位）的比率为多少？

(A) 1 : 6 1 : 6

(B) 7 : 36 7 : 36

(D) 7 : 30 7 : 30

(E) 6 : 25 6 : 25

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The volume is $7 \times 1 = 7$ cubic units. Six of the cubes have $5$ square faces exposed. The middle cube has no face exposed. So the total surface area of the figure is $5 \times 6 = 30$ square units. The ratio of the volume to the surface area is $7:30$.

答案（D）：体积为 $7 \times 1 = 7$ 立方单位。其中有 $6$ 个小立方体各有 $5$ 个正方形面暴露在外。中间的小立方体没有任何面暴露。因此该立体的总表面积为 $5 \times 6 = 30$ 平方单位。体积与表面积之比为 $7:30$。

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