急!! 幾條數學問題!

2008-06-01 6:54 pm

1. A man who is 2 m tall is walking away from a lamppost which is 5 m tall. When he is at a distance d from the lamppost, his shadow is s m long. Give an expression for s in terms of d.

2. A spectator watches a rowing race from the edge of a river bank, standing beside the finish line marker. The lead boat is moving in a straight line that is 36 m from the river bank. Give an expression for d, the distance of the boat from the spectator, in terms of r, the distance remaining in the race.

3. The volume of a sphere is given by the formula V=3/4πr^3, and the surface area is given by the formula S=4πr^2 . Give a formula for the volume of a sphere, V, in terms of S, its surface area. Simplify this formula.

回答 (1)

用戶235087

2008-06-01 7:46 pm

✔ 最佳答案

1. The triangle formed by the feet of the man, his head and the shadow of his head and the triangle formed by the foot of the lamppost, the top of the lamppost and the shadow of the head of the man are similar. Therefore, we have

height of the lamppost：height of the man＝length of the shadow of the man：the distance between the foot of the lamppost and the shadow of the head of the man

＝＞　5/2＝(d＋s)/s
＝＞　5s＝2(d＋s)
＝＞　5s＝2d＋2s
＝＞　s＝2d/3

2. The triangle formed by he spectator, the lead boat and the point on the finish line where the boat is moving towards is a right angle triangle. The right angle is at the point on the finish line. By the Pythagorean theorem, we have

　　　d²＝r²＋36²＝r²＋1296
＝＞　d＝√(r²＋1296)

3.　S＝4πr²　＝＞　r＝√(S/4π)

V＝(4/3)πr³＝(4/3)π[√(S/4π)]³＝(√S)³/(6√π)

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