Math topic中文

Composite solids

problems involving volume and surface area of composite solids

Practice questions

  1. 1A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
  2. 2The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  3. 3The figure shows a solid frustum of height 16 cm cut from a right pyramid with square base. The horizontal top surface h…
  4. 4An 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…
  5. 5In the diagram, ABCDEFGH is a cuboid with dimensions 8 cm by 6 cm by 15 cm. V is the centre of the rectangular base. Sho…
  6. 6Figure 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…
  7. 7The diagram shows two open containers, a right cylinder and an inverted frustum. The right cylinder has a base radius of…
  8. 8The diagram shows a cardboard in the shape of a major sector, centre O and radius 15 cm. The total area of the major sec…
  9. 9The diagram shows a solid formed from a cone, a cylinder and a hemisphere. The cone has base radius 1.5x1.5x cm and height…
  10. 10The diagram shows a cylindrical container used to dispense coffee in a hotel. Calculate the volume of the cylinder. Answ…
  11. 11A 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…
  12. 12Gillian wants to make cylindrical soy wax candles as farewell gifts for 50 classmates and friends in school. The diagram…
  13. 13The diagram shows a semicircle, centre O, radius 16 cm. Show that angle AOB = 1.287 radians, correct to 3 decimal places…
  14. 14The diagram shows a solid ornament in the shape of a cylinder with an upright cone cut out at one end and a hemisphere a…
  15. 15A container is a prism with a cross section in the shape of a right-angled triangle. The container has a height of 12 cm…
  16. 16一个长方体是由三个同样大小的正方体拼成的．已知这个长方体的表面积是5656平方厘米．原来每个小正方体的表面积是 ___ 平方厘米，体积是 ___ 立方厘米．
  17. 17A model consists of a solid hemisphere attached to a solid cylinder as shown in diagram. The height of the cylinder is 2…
  18. 18A conical container with a diameter of 10 cm and a height of 8 cm is filled with water to a depth of 4 cm. Show that the…
  19. 19A liquid container, 30 cm tall, can be modelled by a frustum, A, placed below a cylinder B, as shown in Figure 1. Figure…
  20. 20The diagram above shows a solid structure that is formed from two identical cones and a cylinder. The cylinder is attach…
  21. 21The diagram shows a container which consists of a cylinder of radius rr cm and height hh cm joined to a hemisphere of…
  22. 22Solid A shows a solid formed by joining a hemisphere of radius rr to one end of a cylinder of height rr. The other end…
  23. 23Here is some information about a grain storage bin. Grain Storage Bin | Item | Value | |---|---| | Height (h) | 6880 mm…