Math topic中文

Ratio areas

ratio of areas of similar plane figures

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. 2The points A, B, C, D and E are shown in the diagram below such that ABC and AED are straight lines and BE = 8\sqrt{8}…
  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. 4Diagram 1 shows an equilateral triangle with sides of length 1 unit. An inverted white equilateral triangle with sides o…
  5. 5The diagram shows two circles that touch at C. A, B and C are points on the small circle, centre P. C, D and E are point…
  6. 6The diagram shows an inverted hollow paper cone with a base of radius rr cm and a height of hh cm. The cone is filled…
  7. 7已知两个相似三角形的相似比为2：3，其中一个小三角形的面积为4，那么另一个大三角形的面积为 ．
  8. 8In the diagram, ABCD is a rectangle. OAB is a sector of a circle, centre O. OXD and OYC are straight lines. Show that tr…
  9. 9The diagram below shows two circles, with the same centre at O. Points A, B and C lie on the bigger circle and point D l…
  10. 10A manufacturer sells drinks in bottles of two sizes that are geometrically similar. Some specifications for the bottles…
  11. 11Roy made a model of his yacht with a scale of 1 : 40. The actual length of the yacht is 12.5 m, find the length of the m…
  12. 12The diagram shows two geometrically similar containers. The cost of painting the base area of the smaller container is 2564\frac{25}{64}…
  13. 13△ABC\triangle ABC与△A′B′C′\triangle A′B′C′是位似图形，且△ABC\triangle ABC与△A′B′C′\triangle A′B′C′的位似比是11：22，已知△ABC\triangle ABC的…
  14. 14Two empty paper cups are geometrically similar. The thickness of the paper used is negligible. The big cup can be filled…
  15. 15In the diagram, ABAB is the diameter of the circle. AED and ABC are straight lines. AE=12AE = 12 cm and EB=16EB = 16 cm. ∠ADC\angle ADC…
  16. 16Three tin containers are geometrically similar. The heights of tin container A and tin container C are 8 cm and 16 cm re…
  17. 17A container is a prism with a cross section in the shape of a right-angled triangle. The container has a height of 12 cm…
  18. 18A microprocessor is in the shape of a cube where the sides are 5 mm in length. Find the maximum number of microprocessor…
  19. 19ABCD is a trapezium. F is a point on CD such that ABCF is a rhombus and 3AE=2EF3AE = 2EF. Show that triangles ABE and FDE are…
  20. 20The following diagram shows 2 geometrically similar boxes of cereals of the same brand. Show that the cost of the cereal…
  21. 21已知△ABC\triangle ABC与△DEF\triangle DEF相似，且对应边的比为2\sqrt{2}：11，则△ABC\triangle ABC与△DEF\triangle DEF的面积比为()(\quad) A…
  22. 22A manufacturing company produces electronic components for various devices. They are analyzing the production data for t…
  23. 23John made a triangular poster for the coming mathematics competition. It was in the shape of an equilateral triangle wit…
  24. 24A cylinder X has radius, rr cm and height hh cm. A hemisphere S is such that its radius is half of the radius of cylin…
  25. 25The figure shows a rectangle ABCD with AD = 15 cm. E is on DC produced such that DE = 8 cm. The area of shaded part X is…
  26. 26一个三角形的面积是4.5dm24.5dm^{2}，如果高和底都扩大到原来的22倍，那么它的面积是 ___ .
  27. 27The base areas of two geometrically similar cones are in the ratio of 9 : 49. If the volume of the bigger cone is 1200 c…
  28. 28ABCD is a parallelogram and G is a point on BD. The line BF produced meets DC at F and AD produced at E. GF is parallel…
  29. 29Roy made a model of his yacht with a scale of 1: 40. The actual length of the yacht is 12.5 m, find the length of the mo…
  30. 30The diagram shows a triangle AGD with the points C and B lying on AD and points E and F lying on GD. It is given that CE//BF//AGCE//BF//AG…
  31. 31The diagram shows a square ABCD. The diagonals of the square intersect at W and X is a point on the diagonal BD. Y lies…