标题: Math problem with an astonoshing answer [打印本页] 作者: Xiangdang 时间: 2007-11-27 04:50 标题: Math problem with an astonoshing answer
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.
www.ddhw.com
作者: Xiangdang 时间: 2007-11-27 04:52 标题: 回复：Math problem with an astonishing answer
Sorry for the typo--Astonishing!
作者: Jenny 时间: 2007-11-27 06:21 标题: hi, friend, if you register a net-name, you could
use "edit" to make correction.
作者: salmonfish 时间: 2007-11-27 06:48 标题: 回复：Math problem with an astonoshing answer
V=4/3(pi)(R-h)*3=4/3(pi)3*3www.ddhw.com
作者: Xiangdang 时间: 2007-11-27 09:47 标题: you mean 4/3(pi)3^3? or =4/3(pi)3**3(FORTRAN WAY)
作者: Xiangdang 时间: 2007-11-27 09:49 标题: 回复：hi, friend, if you register a net-name, you cou
Thanks. Do you have an answer for the question? Good luck.
作者: salmonfish 时间: 2007-11-27 17:24 标题: yap.
yap.
作者: salmonfish 时间: 2007-11-27 18:54 标题: graph.（图）
V=4/3(pi)(R-h)3=4/3(pi)33=36pi
www.ddhw.com
作者: Xiangdang 时间: 2007-11-28 06:31 标题: 回复：yap.
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.
www.ddhw.com
作者: salmonfish 时间: 2007-11-28 06:48 标题: I calculated, and got the answer.
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.www.ddhw.com
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.
作者: salmonfish 时间: 2007-11-28 06:53 标题: i'll show it to you tomorrow. busy tonight.
