2026年统编版适配小学六年级数学暑假衔接卷空间想象与综合证明标准试卷第298套（含答案解析与可打印作答区）

六年级数学暑假衔接卷空间想象与综合证明本卷满分120分考试时间120分钟2026年统编版适配小学六年级数学暑假衔接卷空间想象与综合证明标准试卷第298套（含答案解析与可打印作答区）学校班级姓名考号考试时间：120分钟满分：120分题号范围：1—26题答题说明：请在规定位置作答。选择题只填一个最佳答案；填空题直接写结果；解答题须写出必要步骤、推理理由和单位。诚信提示：独立完成，书写工整，计算过程清楚。可使用直尺、铅笔和草稿纸，不得使用带存储功能的计算工具。题型选择题填空题操作与材料分析题综合解答与证明题分值30分24分24分42分一、选择题（本大题共10小题，每小题3分，共30分）选择题答题栏123456789101.（3分）把一个正方体的六个面分别标上1、2、3、4、5、6。现有展开图如下描述：中间一排从左到右是2、3、4，数字3的上方是1，数字3的下方是6，数字4的右方是5。折成正方体后，与数字3相对的面是（）。A.1B.2C.5D.62.（3分）一个长方体长12厘米、宽8厘米、高5厘米。若只把高增加2厘米，长和宽不变，则体积增加（）。A.96立方厘米B.160立方厘米C.192立方厘米D.672立方厘米3.（3分）用8个棱长1厘米的小正方体拼成一个2×2×2的大正方体。若从大正方体的一个顶点取走1个小正方体，剩下立体图形的表面积与原来大正方体表面积相比（）。A.减少3平方厘米B.增加3平方厘米C.不变D.增加6平方厘米4.（3分）一个圆柱的底面半径是3厘米，高是10厘米；一个圆锥与它等底等高。圆锥体积是圆柱体积的（）。A.1/2B.1/3C.2/3D.3倍5.（3分）一张长24厘米、宽18厘米的长方形纸，要剪成尽可能大的同样大小正方形且没有剩余。每个小正方形的边长应是（）。A.3厘米B.4厘米C.6厘米D.12厘米6.（3分）在方格纸上，一个三角形的三个顶点分别为A(1,1)、B(5,1)、C(1,4)。把它绕点A顺时针旋转90°，点C的新位置是（）。A.(4,1)B.(1,-2)C.(4,4)D.(-2,1)7.（3分）一个无盖长方体鱼缸长50厘米、宽30厘米、高40厘米。计算制作玻璃所需面积，应使用（）。A.50×30×40B.2×(50×30+50×40+30×40)C.50×30+2×(50×40+30×40)D.2×(50+30+40)8.（3分）甲、乙两个三角形等底等高。下列说法一定正确的是（）。A.周长相等B.面积相等C.形状相同D.三条边都相等9.（3分）一个长方体包装盒的长、宽、高分别是10厘米、6厘米、4厘米。沿棱剪开展平后，展开图总面积应为（）。A.240平方厘米B.248平方厘米C.280平方厘米D.320平方厘米10.（3分）一只小虫从长方体盒子前面左下角爬到后面右上角。盒子长8厘米、宽6厘米、高4厘米。若只允许在盒子表面爬行，下列展开方式中路径最短对应的长度是（）。A.√(14²+4²)厘米B.√(12²+6²)厘米C.√(10²+8²)厘米D.√(16²+4²)厘米

二、填空题（本大题共6小题，每小题4分，共24分）11.（4分）一个棱长6厘米的正方体，表面积是________平方厘米；体积是________立方厘米。________________________________________________________________________________________________________________________________________________________________12.（4分）一个圆锥形沙堆底面积是18平方米，高1.5米，它的体积是________立方米。________________________________________________________________________________________________________________________________________________________________13.（4分）把一个长18厘米、宽12厘米的长方形按3:2放大后，得到的新长方形周长是________厘米，面积是________平方厘米。________________________________________________________________________________________________________________________________________________________________14.（4分）用27个棱长1厘米的小正方体拼成一个大正方体，把大正方体外表面全部涂黑。恰好有两面涂黑的小正方体有________个。________________________________________________________________________________________________________________________________________________________________15.（4分）在比例尺1:500的校园平面图上，长方形操场长8厘米、宽5厘米。操场实际面积是________平方米。________________________________________________________________________________________________________________________________________________________________16.（4分）两个圆柱的底面半径比是2:3，高的比是3:2，则体积比是________。________________________________________________________________________________________________________________________________________________________________

三、操作与材料分析题（本大题共4小题，每小题6分，共24分）17.（6分）纸盒设计。某小组用一张长方形硬纸板制作无盖长方体笔筒。底面长12厘米、宽8厘米，高10厘米。请完成下列问题。项目所需面面积底面1个长方形12×8长侧面2个长方形2×12×10宽侧面2个长方形2×8×10（1）制作这个无盖笔筒至少需要硬纸板多少平方厘米？（2分）（2）如果在四周外侧贴一圈装饰纸，装饰纸高度为6厘米，至少需要多少平方厘米？（2分）（3）说明为什么无盖笔筒不能直接用长方体表面积公式2(ab+ah+bh)求材料面积。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________18.（6分）积木观察。桌面上摆着若干个同样的小正方体，俯视位置和每个位置的层数如下表，0表示该位置没有小正方体。位置左列中列右列前排层数210后排层数112（1）这个立体图形一共用了多少个小正方体？（2分）（2）从正面看，三列最高层数分别是多少？从左面看，前后两排最高层数分别是多少？（2分）（3）从上面看能看到几个小正方形？说明为什么不能把正面、左面、上面看到的数量相加当作小正方体总数。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________19.（6分）校园花坛。长方形花坛ABCD的长为18米、宽为12米。在AB边上取点E，使AE:EB=1:2；在CD边上取点F，使DF:FC=1:2，连接EF，把花坛分成左、右两块。（1）左侧四边形AEFD的面积是多少平方米？（2分）（2）右侧四边形EBCF的面积是多少平方米？（2分）（3）不用逐块计算，说明两块面积比为什么等于1:2。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________20.（6分）阅读材料。割补法常用于证明图形面积相等：把一个图形剪开并移动，若不重叠、不遗漏地拼成另一个图形，则面积不变。现有一个平行四边形，底为14厘米，高为9厘米。沿一条高剪下左边的直角三角形，平移到右边，可以拼成长方形。请回答：（1）拼成长方形后，长和宽分别是多少？面积是多少？（2分）（2）用割补法说明平行四边形面积公式“底×高”的道理。（2分）（3）若把底扩大到原来的3/2，高缩小到原来的2/3，面积怎样变化？说明理由。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

四、综合解答与证明题（本大题共6小题，共42分）21.（6分）一个长方体水箱从里面量长40厘米、宽25厘米、高30厘米，原来水深18厘米。把一块完全浸没且不吸水的石块放入水箱后，水面升高到20.4厘米。求石块体积，并说明计算依据。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________22.（6分）一个圆柱形容器的底面直径为20厘米，水深12厘米。把水全部倒入一个与它等底的圆锥形容器中，刚好装满。求这个圆锥形容器的高，并写出圆柱与圆锥体积关系的推理过程。________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________23.（7分）两种长方体礼盒内部容积都为960立方厘米。甲盒长20厘米、宽8厘米、高6厘米；乙盒长16厘米、宽10厘米、高6厘米。若都做成有盖包装盒，外包装纸不计接缝损耗。（1）分别求甲、乙礼盒的表面积。（4分）（2）若只从节省包装纸角度选择，应选哪一种？（1分）（3）结合数据说明：体积相同的长方体，表面积不一定相同。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________24.（7分）长方体盒子长12厘米、宽9厘米、高5厘米。点P在前面左下角，点Q在后面右上角。小虫只能沿盒子表面从P爬到Q。（1）写出三种把相邻两个面展开成一个长方形的路径长度表达式。（3分）（2）比较三种长度，求最短路径长。（2分）（3）说明为什么不能直接用空间对角线作为表面最短路。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________25.（8分）如文字描述作图：长方形ABCD中，AB=18厘米，BC=10厘米。点E在AB上，AE=6厘米；点F在CD上，CF=6厘米，连接DE、EF、FB。（1）求四边形AEFD的面积。（2分）（2）求三角形EFB的面积。（2分）（3）证明三角形ADE与三角形BCF面积相等。（2分）（4）若E、F分别在AB、CD上同时向右平移相同距离，且仍在边上，说明四边形AEFD面积怎样变化。（2分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________26.（8分）压轴综合。用若干个棱长1厘米的小正方体拼成一个长3厘米、宽3厘米、高2厘米的长方体，并把外表面全部涂黑。（1）一共用了多少个小正方体？外表面积是多少平方厘米？（2分）（2）恰有三面涂黑、两面涂黑、一面涂黑的小正方体分别有多少个？（3分）（3）如果从长方体上表面正中位置取走一个小正方体，使它原来在上表面、但不在任何棱上，新的立体图形表面积比原来增加还是减少？增加或减少多少？（2分）（4）说明分类统计时为什么不能只看一个面上的涂色情况。（1分）作答区：________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________整卷草稿与检查区（不计分）可用于演算、画展开示意、检查单位与推理步骤。_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________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参考答案与解析一、选择题答案与解析1.C。解析：以3为中心折叠，1与6在相对方向，2与4在相对方向，剩下5与3相对，所以选C。2.C。解析：体积增加量只与增加的高有关，底面积为12×8=96平方厘米，高增加2厘米，增加体积96×2=192立方厘米。3.C。解析：原顶点处外露3个小面被取走，同时露出原来被遮住的3个内侧小面，一减一增相同，表面积不变。4.B。解析：等底等高的圆锥体积是圆柱体积的1/3，所以选B。5.C。解析：要剪成尽可能大的正方形且无剩余，边长为24和18的最大公因数6厘米。6.A。解析：C相对A的位移是向上3格。顺时针旋转90°后变为向右3格，故C的新位置为(4,1)。7.C。解析：无盖鱼缸有底面和四个侧面，面积为50×30+2×(50×40+30×40)。8.B。解析：三角形面积=底×高÷2，等底等高时面积相等；周长和形状不一定相同。9.B。解析：长方体表面积为2×(10×6+10×4+6×4)=2×124=248平方厘米。10.C。解析：表面最短路要把相邻面展开成平面比较。三种主要情形为√((8+6)²+4²)、√((8+4)²+6²)、√((6+4)²+8²)，分别是√212、√180、√164，其中√164最小，即√(10²+8²)。二、填空题答案与解析11.答案：216；216。解析：正方体表面积=6×6×6=216平方厘米，体积=6×6×6=216立方厘米。12.答案：9。解析：圆锥体积=底面积×高÷3=18×1.5÷3=9立方米。13.答案：90；486。解析：按3:2放大，长为18×3/2=27厘米，宽为12×3/2=18厘米；周长=(27+18)×2=90厘米，面积=27×18=486平方厘米。14.答案：12。解析：3×3×3正方体中，两面涂黑的小正方体在棱的中间位置。每条棱有3个小正方体，除去两个顶点后每条棱有1个，共12条棱，所以有12个。15.答案：1000。解析：图上8厘米表示实际8×500=4000厘米=40米；图上5厘米表示实际25米。实际面积=40×25=1000平方米。16.答案：2:3。解析：圆柱体积与半径平方和高成正比，体积比=(2²×3):(3²×2)=12:18=2:3。三、操作与材料分析题答案与解析17.（1）12×8+2×12×10+2×8×10=96+