AMC 8 1993 Problem 17

AMC8 1993 年第 17 题

立体几何★★★☆☆

Square corners, 5 units on a side, are removed from a 20 unit by 30 unit rectangular sheet of cardboard. The sides are then folded to form an open box. The surface area, in square units, of the interior of the box is

从一个 20 × 30 单位的矩形纸板上切掉四个边长为 5 单位的正方形角。然后将四边折叠形成一个开口的盒子。盒子内部的表面积是多少平方单位？

A.300
B.500
C.550
D.600
E.1000

正确答案 · Correct Answer

解析 · Solution

Solution 1

If the sides of the open box are folded down so that a flat sheet with four corners cut out remains, then the revealed surface would have the same area as the interior of the box. This is equal to the area of the four corners subtracted from the area of the original sheet, which is

((20)(30)-4(5)(5)) = 600-100 = \text{(B)500}

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