Math problem with an astonoshing answer

Xiangdang · 发表于 2007-11-27 04:50:24

This is a very entertaining math problem. The answer is astonishing, if you can get it!

There is a 6 inch-long hole bored through the center of a certain sphere. What is the volume of the rest of the sphere (with the 6 " hole in the center)?

Hint: You are not allowed to use calculus to do it. Good luck.

Xiangdang · 发表于 2007-11-27 04:52:51

Sorry for the typo--Astonishing!

Jenny · 发表于 2007-11-27 06:21:24

use "edit" to make correction.

salmonfish · 发表于 2007-11-27 06:48:06

V=4/3(pi)(R-h)*3=4/3(pi)3*3

Xiangdang · 发表于 2007-11-27 09:47:39

you mean 4/3(pi)3^3 =36 Pi ?

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Xiangdang · 发表于 2007-11-27 09:49:54

Thanks. Do you have an answer for the question? Good luck.

salmonfish · 发表于 2007-11-27 17:24:13

yap.

salmonfish · 发表于 2007-11-27 18:54:59

V=4/3(pi)(R-h)³=4/3(pi)3³=36pi

www.ddhw.com

Xiangdang · 发表于 2007-11-28 06:31:00

Your answer happens to be right. But explain the equation 4/3 *pi*(R-h)^3 and show the steps, if you could.

I will tell you very interesting solution procedure.

salmonfish · 发表于 2007-11-28 06:48:06

What do you mean "happen" to be right? I did the calculation on a scratch paper. If you want the procedure, I have to redo it.

Basic idea: Volume of sphere V=4/3(pi)R^3 - 2 x Volume of cap=2/3(pi)(3R h^2-h^3) - Volume of the column=2(pi)a^2(R-h) (here a^2=2Rh-h^2), then............the result.

Xiangdang · 发表于 2007-11-28 06:48:15

Please explain your formula. I have trouble understanding (R-h)^3 term. Your answer though is right, I don't want to say that " a blind cat stepped on a dead mouse", haha.

salmonfish · 发表于 2007-11-28 06:53:26

yinyin · 发表于 2007-11-28 07:46:00

www.ddhw.com

yinyin · 发表于 2007-11-28 08:25:24

本题“astonishing”之处在于：

用黄金打造戒指，假设戒指外表是球面上以大圆为对称面的一条球面带，而内表是柱面。如果戒指的宽度给定，则无论多大的戒指也只需同样多的黄金。

当然，戒指越大就越薄。所需黄金恰是以戒指宽度为直径的一颗金珠。

本贴由[yinyin]最后编辑于：2007-11-29 0:6:15

salmonfish · 发表于 2007-11-28 18:40:29

Good point, and thanks for the detailed solution.

Xiangdang · 发表于 2007-11-29 23:38:46

Wonderful expanation. This is the first time I see the connection of it with gold rings. Thanks.

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Math problem with an astonoshing answer

回复：Math problem with an astonishing answer

hi, friend, if you register a net-name, you could

回复：Math problem with an astonoshing answer

you mean 4/3(pi)3^3? or =4/3(pi)3**3(FORTRAN WAY)

回复：hi, friend, if you register a net-name, you cou

yap.

graph.（图）

回复：yap.

I calculated, and got the answer.

回复：graph.（图）

i'll show it to you tomorrow. busy tonight.

不好意思，代三文兄之劳了。（上传后发现有点大了）（图）

回复：Math problem with an astonoshing answer

Good point, and thanks for the detailed solution.

Excellent expanation[:-Q][:-Q]