R12 compare lengths, areas and volumes using ratio notation Quiz: Pearson Edexcel Maths, Unit 3

The 20 questions

1. Two similar shapes have length ratio 2:3. What is the ratio of their areas?

   • 2:3
   • 4:9
   • 6:9
   • 8:27

2. Two similar solids have a length scale factor of 3. What is the volume scale factor?

   • 27
   • 3
   • 9
   • 6

3. If the length scale factor is k, the area scale factor is:

   • √k
   • 2k
   • k
   • k²

4. If the length scale factor is 0.5, the volume scale factor is:

   • 0.5
   • 0.25
   • 1.5
   • 0.125

5. On a map with scale 1:50 000, a distance of 4 cm represents:

   • 20 km
   • 2 km
   • 2 m
   • 200 m

6. Two similar shapes have a length ratio of 1:4. What is the ratio of their areas?

   • 1:4
   • 1:16
   • 1:8
   • 1:2

7. Why are trigonometric ratios constant for a given angle in right-angled triangles?

   • Angles sum to 180
   • Triangles are similar
   • Triangles are congruent
   • Hypotenuse is longest

8. Two similar cubes have side lengths 2 cm and 5 cm. What is the ratio of their volumes?

   • 4:25
   • 10:25
   • 8:125
   • 2:5

9. Two similar tins have heights 4 cm and 10 cm. The smaller tin holds 50 ml. How much does the larger tin hold?

   • 125 ml
   • 250 ml
   • 500 ml
   • 781.25 ml

10. A jug has a height twice that of a similar smaller jug. How many times greater is its capacity?

    • 2 times
    • 8 times
    • 4 times
    • 6 times

11. A scale drawing uses 1 cm to represent 5 m. A room is 7.2 m wide. How wide is it on the drawing?

    • 1.44 cm
    • 36 cm
    • 0.144 cm
    • 14.4 cm

12. A triangle has area 18 cm². A similar triangle has all lengths doubled. What is its area?

    • 36 cm²
    • 72 cm²
    • 9 cm²
    • 144 cm²

13. Two similar solids have volumes 64 cm³ and 216 cm³. What is the ratio of their corresponding lengths?

    • 2:3
    • 4:9
    • 8:27
    • 3:2

14. A smaller triangle has a side of 5 cm. The corresponding side in a similar larger triangle is 8 cm. What is the scale factor from small to large?

    • 1.6
    • 0.625
    • 1.3
    • 3

15. Two similar prisms have surface areas 50 cm² and 200 cm². What is the length scale factor from the smaller to the larger?

    • 8
    • 2
    • 4
    • 0.25

16. Two similar bottles have volumes in ratio 27:64. What is the ratio of their heights?

    • 3:4
    • 27:64
    • 4:3
    • 9:16

17. A ship model is built at scale 1:200. The model's sail area is 0.45 m². What is the real sail area?

    • 2.25 m²
    • 1800 m²
    • 18 000 m²
    • 90 m²

18. Two similar cones have volumes 250 cm³ and 2000 cm³. What is the ratio of their slant heights?

    • 1:3
    • 1:8
    • 1:4
    • 1:2

19. A triangle has sides 3 cm, 4 cm and 5 cm. A similar triangle has hypotenuse 15 cm. What is the area of the larger triangle?

    • 27 cm²
    • 45 cm²
    • 18 cm²
    • 54 cm²

20. Two similar pyramids have surface areas 48 cm² and 108 cm². What is the length scale factor from smaller to larger?

    • 1.25
    • 2.25
    • 1.125
    • 1.5

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