1973 AMC 12 第 8 题

Question

若给一座高

6

英尺的雕像涂漆需要

1

品脱油漆，则以相同厚度给

540

座与原雕像相似、但只有

1

英尺高的雕像涂漆，需要的油漆品脱数为

If

1

pint of paint is needed to paint a statue

6

ft. high, then the number of pints it will take to paint (to the same thickness)

540

statues similar to the original but only

1

ft. high is

90

72

45

30

15

所需油漆随表面积缩放，而不是随体积缩放

Paint required scales with surface area, not volume

每个长度缩小

6

倍时，每座雕像所需油漆按该比例的平方缩小

Reducing every length by a factor of

6

reduces the paint per statue by the square of that factor

一座

1

英尺高的雕像相对于原雕像的线性比例为

\frac{1}{6}

，所以它的表面积与油漆需求都是原来的

\frac{1}{36}

。因此

540

座小雕像需要

540\cdot\frac1{36}=15

品脱油漆。

所以正确答案是 E。

A

1

-ft. statue has linear scale

\frac{1}{6}

relative to the original, so its surface area and paint requirement are

\frac{1}{36}

as large. The

540

small statues therefore require

540\cdot\frac1{36}=15

pints.

Therefore, the correct answer is E.

其他年份的第 8 题