F.2 Maths Questions 20 points @ hzb53jl55v的部落格

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F.2 Maths Questions 20 points

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1 The figure shows an advertising logo which is composed of a circle and a semi-circle, the radius of the circle is 5cm. Find the values of the following ratios.(a) Circumference of the circle -------------------------------------- Arc length of the semi-circle(b) The shaded area ... 顯示更多 1 The figure shows an advertising logo which is composed of a circle and a semi-circle, the radius of the circle is 5cm. Find the values of the following ratios. (a) Circumference of the circle -------------------------------------- Arc length of the semi-circle (b) The shaded area ------------------------------------- The are of the semi-circle 圖 http://i.imgur.com/2E6OQ.jpg 2 A cylindrical pen holder of base radius 4cm, height 12.5cm does not have a lid. (a) Find the total external surface area of the pen holder. (b) Find the volume of the pen holder. 圖 http://i.imgur.com/j3iUb.jpg 3 May makes a dozen small candles melt and recast if into a large cylindrical candle of height 20cm. If each small candle is a cylinder of radius 1cm and height 9cm, find the radius of the large candle formed. 4 In the figure, OAB is a sector of radius r and arc length l, and < CDE is a triangle of height r and base length l. Prove that the area of sector OAB is equal to the area of
最佳解答:

圖片參考：http://imgcld.yimg.com/8/n/HA00526499/o/701208270078013873421410.jpg 圖片參考：http://imgcld.yimg.com/8/n/HA00526499/o/701208270078013873421411.jpg 圖片參考：http://imgcld.yimg.com/8/n/HA00526499/o/701208270078013873421422.jpg I hope the solution can help you^^” 2012-08-27 19:51:16 補充： http://upload.lsforum.net/users/public/p16980q24s165.png http://upload.lsforum.net/users/public/u13951q25o165.png http://upload.lsforum.net/users/public/w4664Q26m165.png

其他解答:

1. (a) Circumference of the circle=2π(5)=10πcm Arc length of the semi-circle=2π(5x2)/2=10πcm ∴Circumference of the circle/Arc length of the semi-circle=10π/10π=1 (b) The shaded area=π(5x2)^2/2-π(5)^2=25πcm^2 The area of the semi-circle=π(5x2)^2/2=50πcm^2 ∴The shaded area/The area of the semi-circle=25π/50π=1/2 2. (a) The total external surface area =2π(4)(12.5)+π(4)^2 =116πcm^2 or 364cm^2(corr.to 3 sig.fig.) (b)The volume of the pen holder =π(4)^2(12.5) =200πcm^3 or 628cm^3(corr.to 3 sig.fig.) 3. Total volume of a dozen small candles =π(1)^2(9)x12 =108πcm^3 ∴The radius of the large candle =√(108π/20π) =2.32cm(corr.to 3 sig.fig.) 4. Let ∠AOB be θ and l be the length of arc. 2πrθ/360=l θ=180l/πr ∴The area of the sector =πr^2 x (180l/πr)/360 =rl/2 cm^2 The area of the triangle =rl/2 cm^2 ∴The area of the sector=The area of the triangle