第二十九章投影与视图达标测试卷（word版含答案）

第二十九章达标测试卷
一、选择题(每题3分，共30分)
1．下列立体图形中，主视图是三角形的是(　　)
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2．如图所示是某个几何体的三视图，该几何体是(　　)
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A．圆柱
B．球
C．圆锥
D．棱锥
3．在下列四幅图形中，表示同一时刻两棵小树在阳光下的影子的图形可能是(　　)
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4．如图所示的几何体的俯视图是(　　)
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　　　　　　INCLUDEPICTURE"JR158.tif"
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5．【教材P89探究变式】在一个晴朗的上午，乐乐拿着一块矩形木板在阳光下做投影实验，矩形木板在地面上形成的投影不可能是(　　)
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6．如图所示是由6个大小相同的立方体组成的几何体，在这个几何体的三视图中，是轴对称图形的是(　　)
A．主视图
B．左视图
C．俯视图
D．主视图和俯视图
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(第6题)
(第7题)　
　　
　
(第8题)　
　　　
(第10题)
7．如图是一个几何体的三视图，根据图中提供的数据(单位：cm)可求得这个几何体的体积为(　　)
A．2
cm3
B．4
cm3
C．6
cm3
D．8
cm3
8．如图，一个几何体由5个大小相同、棱长为1的正方体搭成，下列关于这个几何体的说法正确的是(　　)
A．主视图的面积为5
B．左视图的面积为3
C．俯视图的面积为3
D．三种视图的面积都是4
9．如图，在一条笔直的小路上有一盏路灯，晚上小雷从点B处径直走到点A处时，小雷在灯光照射下的影长y与行走的路程x之间的函数图象大致是(　　)
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10．如图是某几何体的三视图，根据图中数据，可得该几何体的体积为(　　)
A．9π
B．40π
C．20π
D．16π
二、填空题(每题3分，共24分)
11．工人师傅要制造某一工件，他想知道工件的高，需要看三视图中的__________或__________．
12．如图，将△ABC绕AB边所在直线旋转一周所得的几何体的主视图是图中的__________(填序号)．
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(第12题)
　　　　
(第13题)
13．某校数学兴趣小组为测量学校旗杆AC的高度，在点F处竖立一根长1.5
m的标杆DF，如图所示，量出DF的影子EF的长度为1
m，再量出旗杆AC的影子BC的长度为6
m，那么旗杆AC的高度为________m.
14．一张桌子上重叠摆放了若干枚面值一元的硬币，从三个不同方向看它得到的平面图形如图所示，那么桌上共有________枚硬币．
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(第14题)　　
(第15题)　
　
(第16题)
15．【教材P103习题T10变式】如图是某圆锥的主视图和左视图，该圆锥的侧面积是________．
16．如图，在某一时刻，太阳光线与地面成60°的角，一个皮球在太阳光照射下的投影长为10
cm，则这个皮球的直径是________cm.
17．如图，在平面直角坐标系内，一点光源位于A(0，5)处，线段CD⊥x轴，垂足为点D，C点坐标为(3，1)，则CD在x轴上的影长为________，点C的影子B的坐标为____________．
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(第17题)　　　　　　　　
(第18题)
18．如图是由若干个相同的小立方体搭成的几何体的俯视图和左视图，则组成这个几何体的小立方体的个数可能是____________．
三、解答题(19，20，24题每题10分，其余每题12分，共66分)
19．如图，AB和DE是直立在地面上的两根立柱，AB＝4
m，某一时刻AB在阳光下的投影BC＝3
m.
(1)请你在图中画出此时DE在阳光下的投影；
(2)在测量AB的投影时，同时测量出DE在阳光下的投影长为8
m，请你计算DE的长．
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20．如图，几何体的三种视图有无错误？如果有，请改正．
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21．由几个相同的棱长为1的小立方块搭成的几何体的俯视图如图①所示，方格中的数字表示该位置的小立方块的个数．
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(1)请在上面方格纸(如图②)中分别画出这个几何体的主视图和左视图．
(2)根据三视图，请你求出这个几何体的表面积．
22．小明的身高如图中线段AB所示，在路灯下，他在地面上的影子如图中线段AC所示，小亮的身高如图中线段FG所示，路灯灯泡在线段DE上．
(1)请你确定灯泡所在的位置，并画出小亮在灯光下形成的影子；
(2)如果小明的身高AB＝1.6
m，他的影子长AC＝1.4
m，且他到路灯的距离AD＝2.1
m，求灯泡的高．
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23．如图所示为一几何体的三视图．
(1)写出这个几何体的名称；
(2)任意画出这个几何体的一种表面展开图；
(3)若三视图中的长方形的长为10
cm，正三角形的边长为4
cm，求这个几何体的侧面积．
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24．如图，花丛中有一根路灯杆AB，在灯光下小明在点D处的影长DE＝3
m，沿BD方向行走到达点G，测得DG＝5
m，这时小明的影长GH＝5
m．如果小明的身高为1.7
m，求路灯杆AB的高度．
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答案
一、1.B　2.C　3.D　4.D　5.C　6.D
7．A　8.B　9.C
10．B　点拨：观察三视图可知，该几何体为空心圆柱，其底面内圆半径为2，外圆半径为3，高为8，所以其体积为8×(π×32－π×22)＝40π.
二、11.主视图；左视图　12.②　13.9
14．11　15.20π　16.15
17.；
18．5或6或7　点拨：由俯视图易得，最底层有4个小立方体，由左视图易得，第二层最多有3个小立方体，最少有1个小立方体，那么组成这个几何体的小立方体的个数可能是5或6或7.
三、19.解：(1)如图，连接AC，过点D作DF∥AC，交直线BC于点F，线段EF即为DE的投影．
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(2)∵AC∥DF，
∴∠ACB＝∠DFE.
∵∠ABC＝∠DEF＝90°，
∴△ABC∽△DEF.
∴AB∶DE＝BC∶EF.
∵AB＝4
m，BC＝3
m，EF＝8
m，
∴4∶DE＝3∶8.
∴DE＝
m.
20．解：主视图对，左视图错，俯视图错，如图所示．
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21．解：(1)如图所示．
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(2)这个几何体的表面积为(3＋4＋5)×2＝24.
22．解：(1)如图，点O为灯泡所在的位置，线段FH为小亮在灯光下形成的影子．
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(2)由已知可得＝，
∴＝，
∴OD＝4
m.
答：灯泡的高为4
m.
23．解：(1)这个几何体是正三棱柱．
(2)如图所示．(答案不唯一)
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(3)S侧＝3×4×10＝120(cm2)．
24．解：由题意，得AB⊥BH，CD⊥BH，FG⊥BH.
在△ABE和△CDE中，
∵AB⊥BH，CD⊥BH，
∴CD∥AB.
∴△ABE∽△CDE.
∴＝.
同理可得△ABH∽△FGH，
∴＝.
又∵CD＝FG＝1.7
m，
∴＝.
∵DE＝3
m，DG＝5
m，GH＝5
m，
∴＝，
解得BD＝7.5
m.
∴AB＝＝＝5.95(m)．
答：路灯杆AB的高度为5.95
m.