1) In the figure, the angle of the sector OAB is "theatre" and the
radius of the sector is r cm.If the area of the sector is 20cm and
the length of arc AB is8 cm,find "theatre" and r.
picture: http://img167.imagevenue.com/loc990/th_21072_011_122_990lo.jpg
2) In the figure,the sector OAC with centre O is cut out from a square copper foil OABC
of side r cm. What percentage of the whole copper foil cut out?
picture: http://img215.imagevenue.com/loc582/th_21335_254_122_582lo.jpg
Area of sector
2008-05-20 4:45 am
回答 (1)
2008-05-20 7:55 am
✔ 最佳答案
1) name T as theatreArea:
20 = r^2 x 3.14 x t/360
r^2 x t = 2293 ...(1)
Length:
8 = 2r x 3.14 x t/360
r x t = 458.6 ...(2)
Put (2) into (1)
r (458.6) = 2293
r = 5 (cm)
Put r = 5 into (1)
5^2 x t = 2293
t = 2293/25
= 91.7 (degree)
2) area of square = r^2
area of section OAC
= r^2 x 3.14 x 1/4
= r^2 x 0.785
% of shaped area to the whole square
= [(r^2 - 0.783r^2)/r2] x 100%
= 0.217 x 100%
= 21.7%
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