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
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Arc length of the semi-circle
(b) The shaded area
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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 <CDE.
圖 http://i.imgur.com/KFq7T.jpg 下面果個
F.2 Maths Questions 20 points
2012-08-28 3:33 am
回答 (2)
2012-08-28 3:50 am
✔ 最佳答案
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
參考: I hope the solution can help you^^”
2012-08-28 4:09 am
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
(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
參考: me
收錄日期: 2021-04-16 14:59:26
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