F.2 Maths - Ans.fyi 參考答案

F.2 Maths

2009-09-02 3:57 am

Take the stored value of "pi"in the calculator,and give the answers correct to 2 decimal places if necessary.

1. A metal rod is melted and recast to a new rod.If the length of the new rod is doubled,find the ratio of its base radius to the original one.

2. A cylinder has a height of 14cm.Its curved surface area is 1320 cm^2. Take "pi"=22/7 , find its
a. Base radius
b. Volume

3.The minute-hand of a clock is 1.5m long.
a. Find the distance travelled by the tip of the minute-hand in 40 minutes.(Express the answer in terms of "pi")
b. Find the time taken for the tip of the minute-hand to move 4.5"pi"m.

回答 (1)

用戶9112

2009-09-02 6:06 am

✔ 最佳答案

1. Let the original radius be r and the new radius be R
Let the original length be h then the new radius is 2h
Volume of original rod = πr2h
Volume of recasted rod = πR2(2h) = 2πR2h
Since volume is the same, πr2h = 2πR2h
r2 = 2R2
r = 1.41R
R : r = 1 : 1.41
2. a. Area of curved surface = 2πrh
= 2(22/7)r(14)
= 88r = 1320
r = 1320 / 88
Base radius r = 15cm
b. Volume = πr2h
= (22/7)(15)(15)(14)
= 9900cm3
3. a. One hour = 60 minutes
40 minutes = 40/60 of an hour
The tip of the minute hand will travel in 1 hour the distance 2πr = 2π(1.5) = 3π m
In 40 minutes, it will travel 3π(40/60) = 2π m
b. Since 1 hour corresponds to 3π m, 4.5π m corresponds to 4.5π / 3π
= 1.5 hours or 90 minutes

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