1951 AMC 12 第 6 题

Question

已知一个长方体盒子的底面、侧面和正面面积。这三个面积的乘积等于：

The bottom, side, and front areas of a rectangular box are known. The product of these areas is equal to:

盒子的体积

The volume of the box

体积的平方根

The square root of the volume

体积的两倍

Twice the volume

体积的平方

The square of the volume

体积的立方

The cube of the volume

设三条棱长为

l,w,h

Call the three edge lengths

l,w,h

将三个面的面积

lw

、

wh

和

hl

相乘

Multiply the three face areas

lw,

wh,

and

hl

若三条棱长为

l,w,h

，则三个面的面积为

lw

、

wh

和

hl

。它们的乘积为

(lw)(wh)(hl)=l^2w^2h^2=(lwh)^2\text{，}

即体积的平方。

因此，正确答案是 D。

If the edge lengths are

l,w,h,

the three face areas are

lw,

wh,

and

hl.

Their product is

(lw)(wh)(hl)=l^2w^2h^2=(lwh)^2,

the square of the volume.

Thus, the correct answer is D.

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