F.3 Area and Volume

用戶97935

2008-06-14 6:10 am

A metal pendulum weight, of height h cm, consists of a right circular cone and a hemisphere .

The pendulum weight is then melted and part of the metal is recast into three identical small pendulum weights that are similar to the original one. If the total surface area of the three small pendulum weights is 20% more than that of the original pendulum weight,

(a)find the height of the small pendulum weight in terms of h,

(b)the percentage decrease in the height.

回答 (1)

Uncle Michael

2008-06-14 9:49 am

✔ 最佳答案

Let h’ be the small height of each of the three small pendulum weights.

圖片參考：http://ndc.hkcampus.net/~ndc-007/080614_pendulum.jpg

(a)
Surface area of original weight : Total surface area of three small weight
= 100% : 120%
= 5 : 6

Surface area of original weight : Surface area of each small weight
= 5 : 6/3
= 5 : 2

Hence, h : h’ = √5 : √2
h’ = (√2/√5)h
Height of the small pendulum weight = (√0.4)h
(or 0.6325h)

=====
(b)
Decrease in height
= h - h’
= h - (√0.4)h

Percentage decrease in height
= [(h - √(0.4)h)/h] x 100%
= 100[1 - √(0.4)]%
(or 36.75%)

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