Math topic中文

Volume surface area solids

volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere

Practice questions

  1. 1A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  2. 2Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area o…
  3. 3Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm6\text{ cm} in diameter and 12 cm12\text{ cm}…
  4. 4把一个长方体正好分割成两个完全相同正方体，若分割后的正方体的棱长为4cm，则分割后比分割前表面积增加了 ，总体积增加了 ．
  5. 5The figure below is made up of 1-cm cubes. What is the volume of the figure? Ans : ___ cm3\text{cm}^3
  6. 6已知圆锥的底面半径为5cm，母线长为9cm，则它的侧面积为 ．
  7. 7The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  8. 8Calculate the total surface area of a solid hemisphere with radius 6 cm. Answer ... cm^2
  9. 9In the cube ABCDEFGHABCDEFGH with opposite vertices CC and EE, JJ and II are the midpoints of edges FB‾\overline{FB} and HD‾\overline{HD}…
  10. 10学校要粉刷一间教室的四壁和屋顶，除去门窗和黑板的面积24平方米，己知教室长8米，宽6米，高4米，要粉刷的面积是多少平方米？
  11. 11The figure shows a solid frustum of height 16 cm cut from a right pyramid with square base. The horizontal top surface h…
  12. 12一种汽车每千米需用油0.1升，它的油箱是长50厘米，宽40厘米，高30厘米的长方体，将它的油箱加满油可行多少千米？
  13. 13亮亮家的客厅长6m6m，宽4m4m，高3m3m，门窗总面积9m29m^{2}，现在要把客厅的四壁和顶面粉刷环保油漆，刷油漆的面积是多少平方米？
  14. 14An industrial mixer is made up of an open cylinder connected to a cone. The height of the cylinder and the cone is 1.2 m…
  15. 15一个长方体小水箱，长10分米，宽8分米，高5分米． （1）做这个水箱至少需要多少平方分米的铁皮？ （2）如果1立方分米的水重1千克，那么这个水箱能装多少千克的水？
  16. 16水池AA，BB，CC都是长方体，深为1.6m1.6m，底部尺寸为3m×4m.13m×4m.1号阀门24min⁡24\min可将无水AA池注满；22号阀门用来从AA池向BB池放水，30min⁡30\min可将AA…
  17. 17一个长方体的木箱，长1.2m，宽0.8m，高0.6m．做这个木箱至少要用多少平方米木板？
  18. 18Fang Min glued eight 1-cm cubes to form the solid below. She painted the whole solid, including the base. What was the t…
  19. 19The diagram shows a right circular cone cut from a solid steel sphere. Point O is the centre of the sphere with radius 1…
  20. 20The figure above shows a solid. The cross-section of the solid is a sector of a circle of radius 5 cm and angle 30°. The…
  21. 21A composite solid is made from a cylinder and two hemispheres. The cylinder has radius pp and length 2p2p, while the he…
  22. 22一个正方体容器的棱长是4厘米，装满水后倒入另一个深6厘米的圆锥形容器中，刚好倒满，这个圆锥形容器的底面积是 ．
  23. 23Figure I shows a piece of wood is in the form of a right circular cone with a base diameter of 18 cm. The curved surface…
  24. 24把一块不规则的石块放入一个棱长为10厘米的正方体容器里，水面上升了6厘米，求石块的体积．
  25. 25用硬纸做一个长为10厘米，宽为8厘米，高为4厘米的长方体模型，至少需要多少硬纸？
  26. 26Jill glued 12 cubes of side 1 cm to form a solid as shown below. (Top view, Side view and Front view are indicated on th…
  27. 27The diagram shows a pyramid with a rectangular base and its height is 9 cm. The volume of the liquid in the pyramid is 23\tfrac{2}{3}…
  28. 28在一个长40厘米、宽25厘米的长方体水槽中浸没一个长方体金属块，这时水槽中水面的高度是20厘米，把金属块取出后，水面高度降低到16厘米．已知金属块长25厘米，宽16厘米，高是多少厘米？
  29. 29The diagram shows two open containers, a right cylinder and an inverted frustum. The right cylinder has a base radius of…
  30. 30The diagram shows a cardboard in the shape of a major sector, centre O and radius 15 cm. The total area of the major sec…
  31. 31一个长方形铁皮长30cm，宽25cm，从四个角各切掉一个长为5cm的正方形，然后做成一个无盖的盒子，这个盒子用了多少铁皮？它的容积是多少？
  32. 32用铁丝做一个长6分米、宽5分米、高2分米的长方体框架，至少需要铁丝 分米；把6个面都糊上彩纸，至少需要彩纸 平方分米．
  33. 33A book writer intends to sell her books to either Australia or Brazil, and she is planning to use Singapore post office…
  34. 34The diagram shows a solid formed from a cone, a cylinder and a hemisphere. The cone has base radius 1.5x1.5x cm and height…
  35. 35两个正方体的棱长比是3：5，这两个正方体的体积比是( )。 A. 27：125 B. 9：25 C. 3：5 D. 无法计算
  36. 36一个棱长总和是80cm的长方体，刚好可以分成3个相同的小正方体，原来长方体的体积是多少立方厘米？
  37. 37The diagram shows a cylindrical container used to dispense coffee in a hotel. Calculate the volume of the cylinder. Answ…
  38. 38A hot water tank is made by joining a hemisphere of radius 30 cm to a cylinder of radius 30 cm and height 70 cm. Calcula…
  39. 39Gillian wants to make cylindrical soy wax candles as farewell gifts for 50 classmates and friends in school. The diagram…
  40. 40用若干个同样的小正方体拼成一个较大的正方体，至少需要()(\quad)个． A. 99 B. 88 C. 44
  41. 41The diagram shows a semicircle, centre O, radius 16 cm. Show that angle AOB = 1.287 radians, correct to 3 decimal places…
  42. 42一个正方形的棱长总和与一个长方形的棱长总和相等，则它们的体积相等． ． （判断对错）
  43. 43ξ={x:x is an integer, 2≤x≤14}\xi = \{x : x \text{ is an integer},\ 2 \le x \le 14\} A={x:x is a prime number}A = \{x : x \text{ is a prime number}\} B={x:x is a multiple of 3}B = \{x : x \text{ is a multiple of 3}\}…
  44. 44A cubical container and Tank Y are shown below. (a) Find the volume of water in the cubical container. (b) Tank Y was fi…
  45. 45一个棱长10cm10cm的正方体切成两个完全一样的长方体，一个长方体的体积是 ___ ，表面积是 ___ .
  46. 46O is the centre of the equilateral triangle. The triangle ABC forms the base of a pyramid. The vertex, X is vertically a…
  47. 47用棱长1cm的小正方体搭一搭． （1）搭一个稍大一些的正方体，至少需要多少个小正方体？ （2）用12个小正方体搭一个长方体，可以有几种不同的搭法？记录搭出的长方体的长、宽、高． （3）搭一个四个面都是正方形的长方体，你发现了什么？
  48. 48A cone has a radius of 24 cm24\ \text{cm} and a total surface area of 1536π cm21536\pi\ \text{cm}^2. Show that the volume of the c…
  49. 49一根长6m6m的长方体木料，锯成两段，表面积增加了80cm280cm^{2}，原来这根木料的体积是 ___cm3cm^{3}。
  50. 50解答下列应用题： (1)某房间的面积为17.6m217.6m^{2}，房间地面恰好由110110块相同的正方形地砖铺成，每块地砖的边长是多少？ (2)已知第一个正方体水箱的棱长是60cm60cm，第二个正方体水箱的体积比第一个水箱的体积的33…
  51. 51由33个棱长是11分米的正方体拼接成的长方体的表面积是()(\quad)平方分米 A. 1818 B. 1616 C. 1414 D. 99
  52. 52一个长方体铁皮水桶高5厘米，它的底面积是8平方分米，这个水桶的容积是 升．
  53. 53The diagram shows a lecture theatre in the shape of a prism with height 9 metres. The floor of the lecture theatre, ABCD…
  54. 54The diagram shows the cross section of a plastic pipe. The arc AB is part of the circle with centre O and radius 45 mm.…
  55. 55挖一个长40米，宽25米，深2米的游泳池． （1）要挖出多少立方米的土？ （2）沿着游泳池的周围走一圈，至少要走多少米？ （3）如果在游泳池的四壁和底面贴边长2分米的正方形瓷砖，需要多少块？
  56. 56若圆锥的底面半径为3cm3cm，母线长为5cm5cm，则这个圆锥的全面积为 ___ cm2.(cm^{2}.(结果保留π)π)
  57. 57一个正方体的棱长总和是72厘米，它的一个面是边长___厘米的正方形，它的表面积是___平方厘米，体积是___．
  58. 58用一根长4848厘米的铁丝，剪断后焊接成一个正方体框架。如果用白纸贴满这个正方体的各个面，至少要用白纸 ___平方厘米，这个正方体的体积是 ___立方厘米。
  59. 59一个长36分米的铁丝能围成一个正方体框架，如果在这个正方体框架外面糊一层纸，需要 平方分米的纸，这个正方体的体积是 立方分米．
  60. 60A closed conical ornament has a circular base of radius 10 cm and height 25 cm, and contains mercury to a depth of 15 cm…