Maths Quiz tmr!!! urgent !

👨🏻‍🏫 學術台數學

[匿名]

2014-02-11 3:05 am

1. About area and volume
the total surface area
if there is a cylindrical hole drilling through a solid cylinder of base radius 2r cm and height r cm .What is the total surface area of the hollow cylinder in terms of pye and r? Simplify yr answer?
(Pls if anyone can imagine the graph,then you can do it ,I am really in a rush to know the steps and calculations ! )
For the two outer dome shape,I mean the formula 2pye r h +2 pye r^2
do I need to calculate according to corresponding sides ?
like if the outer round is of radius 2r,the is that mean I need to use the 2r?
And another case,if the radius of the inner round is r ,then does that mean I need to use the r ?
I am so confused about it !!! ;(

2. (a) Factorize a^4+2a^2b^2+b^4

(b) Hence or otherwise,factorize a^4+a^2b^2+b^4

thank you very much!!! PLS VERY URGENT!!! :(:(:(

更新1:

erm...the inner drill radius is r ,the whole outer one is 2r,that means the space between the inner and the outer is actually r . erm...the height is r already .......no h is involved.... thanks for yr patience !!! ;)

更新2:

I have found a diagram on net...... maybe it surely gives u some ideas

更新3:

haha if available.also answer the above questions topic is % revision thx a million :p

更新4:

I have understood the one u wrote (steps) wait u for reply!

更新5:

oops,I originally made a mistake !!! Thank you so much for yr help,despite the effort spent in washing dishes!;)))

更新6:

argh,I also want to ask a quite minor questions............ if a question mentions that the original price of a property two yrs ago is $$. and then in(a),it requires me to calculate the new price of property after 1 year. then in (b),it requires me to get the growth factor ...

更新7:

and then in (c) ,it tells me that if the growth factor remains constant,find the price of the property after 2 years , should I use the value of the original or the new price after the 1 yr? thank you again two teachers !

更新8:

no need to know the growth factor ,but haha,just to know that whether i should use the related value (a) or the value stated in the original question?Thank you !

回答 (5)

用戶4366

2014-02-11 5:24 am

✔ 最佳答案

You have to give the drill size.

Is it r ?

2014-02-10 19:55:29 補充：
if there is a cylindrical hole drilling through a solid cylinder of base radius 2r cm and height [ r ] cm .

Should it be [ h ] cm ?

2014-02-10 20:22:19 補充：
2. (a) Factorize a^4+2a^2b^2+b^4

(b) Hence or otherwise,factorize a^4+a^2b^2+b^4

a⁴ + 2a²b² + b⁴ = (a²+b²)²

a⁴+a²b² +b⁴
= a⁴+a²b² +b⁴ + a²b² - a²b²
= a⁴+2a²b² +b⁴ - a²b²
= (a²+b²)² - a²b²
= (a²+b²)² - (ab)²

Using the relation that : [ a²-b² = (a+b)(a-b)

= (a²+b²+ab)(a²+b²-ab)

2014-02-10 20:25:32 補充：
I think it is better to use "hollow cylinder" ; try it.

2014-02-10 20:27:20 補充：
我要洗碗，洗完都未有人幫你的話，我就幫你做啦！

2014-02-10 21:24:11 補充：

圖片參考：http://imgcld.yimg.com/8/n/HA00388954/o/20140210211443.jpg

R = 2r

左圖是右圖的頂視圖 (從上向下望)，要計灰色面積

= 大圓 - 細圓 = π(2r)² - π(r)² = 3πr²

底頂共有 2 塊，所以面積為 6πr²

圓柱外表面積 = 2π(2r)(h) = 2π(2r)(r) = 4πr²

圓柱內表面積 = 2π(r)(h) = 2π(r)(r) = 2πr²

總表面積 = (6+4+2)πr² = 12πr²

2014-02-10 21:25:56 補充：
哈哈!!!

今天我比你幸福。

2014-02-10 23:39:02 補充：
對不起，我對 growth factor 無認識，幫不了你。

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Iris

2014-02-14 9:02 am

Hi, did u solve your problem about growth factor?

For example:
Original price is $1000
growth factor is (1+ 10%)

then the first year price should be $1000 * (1+10%)
the second year will be $1000 * (1+10%)^2
其實背後意思係$1000 * (1+10%) * (1+10%)

Growth factor means each year 都會增加呢個percent

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[匿名]

2014-02-14 7:52 am

2. (a) Factorize a^4+2a^2b^2+b^4

(b) Hence or otherwise,factorize a^4+a^2b^2+b^4

ans:
(a) a^4+2a^2b^2+b^4
=(a^2)^2+2(a^2)(b^2)+(b^2)^2
consider a^2 = x and b^2 = y
and we have x^2+2xy+y^2
so (a^2+b^2)^2
(b) a^4+a^2b^2+b^4
=a^4+2a^2b^2+b^4-a^2b^2
=(a^2+b^2)^2-(ab)^2
in fact it is a^2-b^2
so (a^2+b^2+ab)(a^2+b^2-ab)

參考: my brain

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知足常樂

2014-02-11 5:14 am

郭老師，你而家可以洗碗就好啦～

我而家先可以食飯．．． =P

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[匿名]

2014-02-11 4:21 am

not enough space here......type cylindrical cylinder on google and get the third picture on the searcher ......
most similar with mine!!! THXTHX

2014-02-10 20:52:32 補充：
oh thank you so much....haha washing dishes ......add oil!!! xdxdxd

2014-02-10 21:15:39 補充：
why so late??????Masterijk
It's not always healthy having dinner so late!

2014-02-10 22:32:55 補充：
and then in (c) ,it tells me that if the growth factor remains constant,find the price of the property after 2 years ,
should I use the value of the original or the new price after the 1 yr?

thank you again two teachers !

👍 0 👎 0

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