Volume (Proof)

2013-10-12 9:03 pm
A) 求 以下各方程式既proof.

1, Area of sector
2. Arc length
3. Total surface area of prism
4. Volume of cylinder
5. Volume of pyramid

B) Cylinder 既 Curved surface area 同 Total surface area 有咩分別?

回答 (2)

2013-10-17 9:36 pm
✔ 最佳答案
http://www.proofwiki.org/wiki/File:Sector.pngFrom Area of Circle, the area of Circle is pi*r^2.From Full Rotation measures 2 Pi Radians , the angle within Circle is 2pi.The fraction of the area of circle within the sector BAC is therefore pi*r^2*angle of the sector/(2pi)
Hence the result.Then, the formula for a line integral is
圖片參考:http://www.emathzone.com/contents/uploaded/images/geometry/surface-area-cone/clip_image010.gif


圖片參考:http://www.emathzone.com/contents/uploaded/images/geometry/surface-area-cone/clip_image012.gif


圖片參考:http://www.emathzone.com/contents/uploaded/images/geometry/surface-area-cone/clip_image014.gif


圖片參考:http://www.emathzone.com/contents/uploaded/images/geometry/surface-area-cone/clip_image024.gif
Area of base

圖片參考:http://www.emathzone.com/contents/uploaded/images/geometry/surface-area-cone/clip_image027.gif
參考: from google search
2013-10-13 3:45 am
B) Cylinder 既 Curved surface area 同 Total surface area 有咩分別?

Total surface area = Curved surface area + Top Circle Area + Bottom Circle Area


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