✔ 最佳答案
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2014-05-11 14:58:07 補充:
1.a1:a2:a3
=pi*r1^2:pi(r2^2-r1^2):pi(r3^2-r2^2)
=1:4:12.......ans
2014-05-11 15:02:10 補充:
2.承上題,這三個同心圓的半徑比為何?
a1/1=a2/4=a3/12=k
a1=k=pi*r1^2 => r1^2=k/pi
a2=4k
=pi*(r^2-r1^2)
r2^2=a2/pi+r1^2
=4k/pi+k/pi
=5k/pi
a3=pi(r3^2-r2^2)
r3^2=a3/pi+r2^2
=12k/pi+5k/pi
=17k/pi
令k=pi
r1=1(cm)
r2=√5(cm)=2.236(cm)
r3=√17(cm)=4.1231(cm).......ans
2014-05-11 18:58:04 補充:
(1) 補充:
r1,r2,r3=小,中,大圓半徑
a1=小圓面積=pi*r1^2
a2=中圓面積=pi*(r2^2-r1^2)
a3=大圓面積=pi*(r3^2-r2^2)
=> a1:a2:a3=r1^2:(r2^2-r1^2):(r3^2-r2^2)
=反比例
=1:4:12
2014-05-11 19:01:42 補充:
(2) 補充:
連比例可以改為正比例:
a1/1=a2/4=a3/12=k
=> a1=k, a2=4k, a3=12k
a1=k=pi*r1^2 => r1^2=k/pi
a2=4k=pi*(r^2-r1^2)
=> r2^2=a2/pi+r1^2
=4k/pi+k/pi
=5k/pi
2014-05-11 19:05:46 補充:
a3=12k=pi*(r3^2-r2^2)
=> r3^2=a3/pi+r2^2
=12k/pi+5k/pi
=17k/pi
r1^2:r2^2:r3^2=k:5k:17k=1:5:17
=> r1:r2:r3=1:√5:√17
2014-05-12 04:17:14 補充:
1.a1:a2:a3
=pi*r1^2:pi(r2^2-r1^2):pi(r3^2-r2^2)
=1:4:12.......ans
2014-05-12 04:18:12 補充:
上面張貼錯誤
(1) 修正:
a1:a2:a3=反比
=(1/12):(1/4):1
=(12/12):(12/4):12.....同時*12
=1:3:12
2014-05-12 04:18:40 補充:
(2) 修正
正比改為連比:
a1/1=a2/3=a3/12=k^2 => a1=k^2, a2=3k^2, a3=12k^2
k^2=r1^2 => r1=k
3k^2=r2^2-r1^2 => r2^2=3k^2+r1^2=4k^2 => r2=2k
12k^2=r3^2-r2^2 => r3^2=12k^2+4k^2=16k^2 => r3=4k
=> r1:r2:r3=1:2:4