关於數學問題!!!(10分)

2010-11-04 8:13 am

four identical squares of side 4 cm are cut off from the corners of a aquare and the remaining portion is folded to form a box without cover. if the capacity of the box is 40 cm^3, find the length of the side of the original square paper card.

the dimensions of a rectangular picture are 16 cm×20 cm. the piture is surround with a wooden frame of uniform width. if the area of the frame is 252 cm^2, find its width

回答 (1)

用戶2053

2010-11-04 9:15 am

✔ 最佳答案

井Let x be the length of the side of the original square paper card , (x > 4*2 = 8)then each sides of the square base of the box = x - 2*4 = x - 8 cmthe height of the box = x cmthe capacity of the box = height * base area= x (x - 8)^2= 40x (x^2 - 16x + 64) = 40x^3 - 16x^2 + 64x - 40 = 0(x - 10)(x^2 - 6x + 4) = 0x = 10 or x = 3 ± √5 ( < 8 , rejected)The length of the side of the original square paper card is 10 cm.
Let its width be w cm , The area of the frame = (2w + 16)(2w + 20) - (16)(20) = 2522(w + 8) 2(w + 10) - 572 = 0(w + 8)(w + 10) - 143 = 0w^2 + 18w + 80 - 143 = 0w^2 + 18w - 63 = 0(w + 21)(w - 3) = 0w = - 21 (rejected) or w = 3Its width is 3 cm.

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