Maths

👨🏻‍🏫 學術台數學

用戶124294

2008-10-03 12:13 am

The dimensions of a rectangle cardboard are 26cm X16cm .A square of side x cm is cut away from each corner of the cardboard. The remaining part is folded up to form an open box.

a . Express the base area of the open box in terms of x.
b. If the base area of the box is 200cm2 , find the volume of the box.

更新1:

Give me the calculate process.

回答 (2)

用戶10012

2008-10-03 2:51 am

✔ 最佳答案

Length of base = 26 - 2x
Width of base = 16 - 2x
(a)Therefore, area of base = (26-2x)(16-2x) = 4(13-x)(8-x).
(b) 4(13-x)(8-x) = 200
104 - 21x + x^2 = 50
x^2 - 21x + 54 = 0
(x - 18)(x -3) = 0
x = 13 (rej. because length of base will be 0) and x = 3.
Therefore, volume = 200 x 3 = 600 cm^3.

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希雪

2008-10-03 3:03 am

a . Express the base area of the open box in terms of x.

由於四邊的角都cut 左 x cm

(26 - 2x)(16 - 2x)
= 4x^2 - 84x + 416

b. If the base area of the box is 200cm2 , find the volume of the box
4x^2 - 84x + 416 = 200
4x^2 - 84x + 216 = 0
(x - 18)(x - 3) = 0 <==用計數機禁到
x = 3 or x = 18 (rejected) <-- 由於超過了尺寸範圍

Volume:
200 x 3
= 600 cm^3

參考: 自己

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