F.2 Area and Volume! 20 points

2012-04-10 4:24 pm

1) The cross- section of an old tree is circular in shape and has a circumference of 5.2 cm. Find the area of the cross-section.
2) A piece of wire 176cm long is bent into the shape of a circle. Find the area enclosed by the wire.
3) The circumference of a circle and the perometer of a aquare are each 80cm. Which figure has a greater area and by how much?
4) If the ratii of two circles c1,c2,c3 is 3:7, find the rotio of the areas of these two circles.
5) Th area of the shaded sector is 2/5 the wgole cirlcle with centre O. Find the angle of the shaded sector.
6) A wire 30m long is bent to a semi-circle and a diameter as shown. Find the radius of the semi-circle and the area enclosed by the wire.

回答 (1)

Ka ho

2012-04-10 6:18 pm

✔ 最佳答案

1. Area=pi(5.2/2pi)^2
=pi *27.04/4pi^2
=27.04 / 3pi =2.87cm^2(corr.to 3sig.fig)//
2.Area=pi(176/2pi)^2
=pi*30976/4pi^2
=30976/3pi=3290cm^2(corr.to 3sig.fig)//
3.Circle=pi*(80/2pi)^2
=pi*6400/4pi^2
=1600/3pi =170cm^2(corr,to 3sig.fig)//
4.你多左個c3 - -?
The ration of the area of circle 1:that of circle 2
=pi(3)^2 : pi(7)^2
=9:49 //
5.Let x be the angle of the sector.
pi*r^2*(x/360)=pi*r^2*2/5
x/360=2/5
x=2/5 *360=144
The angle of the sector is 144.
6.Let r m be the radius of the semi-circle
30-2r=2*pi*r*1/2
30-2r=pi*r
30=(pi+2)r
r=30/(pi+2)=5.83(corr,to 3sig.fig)
The radius of the semi-circle is 5.83m.
The area of the semi-circle=pi*[30/(pi+2)]^2
=900pi/(pi+2)^2
=107m^2(corr.to 3sig.fig)//

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