第12章与圆相关的区域–练习12.2 |套装1
问题8.用5 m长的绳子将一匹马绑在15 m边的方形草场的一个角上(见图)。找
(i)马匹可以在牧场上放牧的那部分区域。
(ii)如果绳索长10 m而不是5 m，则放牧面积增加。 (使用π= 3.14)
解决方案：
(i) Horse with graze=∅/(360°)*π*r2
=90°/360°*3.14*5*5
=78.5/4
=19.625cm2
Area of circle the length of rope is increased to 10m
=∅/(360°)*π*r2
=90°/360° *3.14*10*10
=314/4=78.5cm2
(ii) Increasing in grazing area=78.5m2-19.635m2=58.875m2
问题9.胸针是用直径35毫米的圆形银线制成的。该线还用于制造5个直径，将圆分成10个相等的扇区，如图所示。查找：
(i)所需的银线的总长度。
(ii)胸针每个扇区的面积。
解决方案：
(i) Total length of silver wire required=circumference of broach+5diameter
=5*35*mm*πd
=175+22/7*35
=175+110
=185mm
(ii) Area of each sector=1/10*Area of circle
=1/10*π*r2
=1/10*22/7*35/2*35*2
=11*35/4
=385/4mm2
问题10.一把雨伞有8个等距分布的肋骨(见图)。假设雨伞是一个半径为45厘米的扁平圆，请找到雨伞的两个连续肋之间的区域。
解决方案：
Total ribs in umbrella=8
Radius of umbrella is =45cm
Area between the two consecutive ribs=1/8π*r2
=1/8*22/7*45*45cm2
=22275/28
问题11.一辆汽车有两个不重叠的刮水器。每个刮水器都有一个长度为25 cm的刮片，扫过115°的角度。查找每次刮刀清洁后的总面积。
解决方案：
Angle made by sector=∅=115°
r=25cm
Total area clean at each sweep of the blades=2*Area of sector
=2*∅/(360°)*π*r2
=2*(115°)/(360°)*22/7*25*25cm2
=23*11*25*25cm2
=158125/126cm2
=1254.96cm2
The total area clean at each sweep of blades=1254.96cm2
问题12：为警告船舶有水下岩石，灯塔将红色的光散布在80°的角度范围内，距离为16.5 km。找到警告船只的海域。
解决方案：
(Use π = 3.14)
Distance over which light fall =r=16.5km
Angle made by the sector=∅=80°
Area of the sea over which the ships are warned=Area of sector
=∅/(360°)*π*r2
=(80°)/(360°)*3.14*16.5*16.5
=1709.73
=189.97km2
The area of ships is +warned =189.97km2
问题13.圆桌盖具有六个相等的设计，如图所示。如果盖的半径为28厘米，在找到的₹0.35速率每cm 2使设计的成本。 (使用√3= 1.7)
解决方案：
Total equal designs==6
Radius =28cm
Cost for making design=RS.035 per cm2
∠O=360°/6=60°
Area of 1 design =Area of sector-Area of triangle
=∅/(360°)*π*r2*–
问题14.在下面的答案中打勾：
半径为R的圆的角度为p(以度为单位)的扇形的面积为
(A)P / 180×2πR(B)的p / 180×πR 2(C)P / 360×2πR(d)P / 720×22πR
解决方案：
Area of sector angle p=p/360*2πr2
Therefore, option (D) is correct.