一d similar solid既問題

2007-01-13 6:55 pm

1.The base areas of two similar cones are 32cm^2 and
50cm^2
a)Find the ratio of the curved surface area of the smaller
cone to that of the larger one.

Ratio of curved surface areas of small cone to the large cone
= 32 : 50
= 16 : 25

點解係16:25既,curved surface area係底面積既1/2咩,唔明????
有冇人可以詳細解釋下?

回答 (1)

myisland8132

2007-01-13 7:13 pm

✔ 最佳答案

先看看正解
Assume the original base area of a right circular cone is A1, the new base area is A2
then
A1/A2=32/50=16/25
so
(r2/r1)^2=16/25
r1/r2=4/5
the ratio of the curved surface area of the smaller cone to that of the larger one
= (r2/r1)^2
=16/25
由以上計算過程可知﹐因為curved surface area和base areas 都是area﹐它們的比都會是邊長比的平方。
不論curved surface area同base area是甚麼關係都一樣 (因為個因子會在相除時抵消了的)

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