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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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國一數學,請詳解.謝謝
Sep 4th 2013, 13:24

直徑比是3:2:1，如你照片上也寫了，底面積比是 9:4:1

為了詳細說明，我設A、B、C直徑分別是3x、2x、x，
所以底面積分別是9x^2、4x^2、x^2

再設水高都是h，所以水的體積分別是9hx^2、4hx^2、hx^2

設每一顆球體積是v

所以A裡放3顆球，體積增加3v，上升a，底面積×上升高 = 增加體積
=> 9x^2．a = 3v
=> a = 1/3 ．v/x^2

B裡放2顆球，體積增加2v，上升b，底面積×上升高 = 增加體積
=> 4x^2．b = 2v
=> b = 1/2 ．v/x^2

C裡放2顆球，體積增加v，上升c，底面積×上升高 = 增加體積
=> x^2．c = v
=> c = 1．v/x^2

所以a : b : c = 1/3 : 1/2 : 1 = 2 : 3 : 6

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