MATHS-- open-ended questions

用戶145604

2007-07-27 11:18 pm

Peter has a wire whici is 40 cm long. He wants to bend it into a shape such that it

encloses a maximum area. Would you help Peter to find the ideal shape he wants?

請幫我解答! thx

呢條題來自 Train Up MATHEMATICS 1 (S.1-S.2)

回答 (1)

Peterr

2007-07-28 7:09 am

✔ 最佳答案

Assumed that Peter would bend the wire into (a) a square; or (b) a circle,
And also assume that the area of a square is the largest among all polygons and that the area of a circle is the largest among all conics.

(a) If the wire is bent into a square,
One side of the square = 40 / 4 = 10
Area of square = 10 * 10 = 100 (sq. cm.)

(b) If the wire is bent into a circle,
Let r cm. be the radius of the circle.
Thus, 2 * 兀 * r = 40
r = 40 / (2 * 兀) = 20 / 兀

Area of circle = 兀 * r^2
= 兀 * (20 / 兀) ^2
= 400 / 兀
= 400 / 3.1416
= 127.32 (sq. cm.)

We can see that a circle shape will enclose a maximum area.

I have tried my best to help you.

2007-07-29 10:47:54 補充：
The answer is simply (circle).希望幫到你.

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