R12 Comparing lengths, areas and volumes using ratio and scale factors Quiz: AQA Maths, Unit 3

The 20 questions

1. Two similar rectangles have lengths in the ratio 2 : 3. What is the ratio of their areas?

   • 6 : 9
   • 4 : 9
   • 2 : 3
   • 8 : 27

2. A cube has side 3 cm and a similar cube has side 6 cm. What is the ratio of their volumes?

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

3. A 2D shape is enlarged by scale factor 4. By what factor does its area change?

   • 4
   • 64
   • 16
   • 8

4. A solid is enlarged by scale factor 3. By what factor does its volume change?

   • 9
   • 81
   • 3
   • 27

5. A model car is made to a scale of 1 : 50. The real car is 4 m long. How long is the model?

   • 80 cm
   • 8 cm
   • 2 cm
   • 8 mm

6. On a map, 1 cm represents 2 km. A distance on the map measures 3.5 cm. What is the real distance?

   • 14 km
   • 7 km
   • 5.5 km
   • 1.75 km

7. Two similar triangles have a length scale factor of 2.5. What is the area scale factor?

   • 6.25
   • 15.625
   • 2.5
   • 5

8. When lengths in two similar shapes are in the ratio k : 1, what is the ratio of their areas?

   • k² : 1
   • k³ : 1
   • 2k : 1
   • k : 1

9. When lengths in two similar solids are in the ratio k : 1, what is the ratio of their volumes?

   • k : 3
   • k³ : 1
   • 3k : 1
   • k² : 1

10. Two similar cylinders have radii 2 cm and 5 cm. What is the ratio of their surface areas?

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

11. A bottle holds 500 ml. A similar bottle has all its lengths doubled. What is its capacity?

    • 4000 ml
    • 2000 ml
    • 1000 ml
    • 8000 ml

12. A tank holds 80 litres. A similar tank is scaled by a factor of 1.5. What is its capacity?

    • 270 litres
    • 120 litres
    • 240 litres
    • 160 litres

13. Rectangle B is similar to rectangle A with scale factor 2. Rectangle B has area 36 cm². What is the area of A?

    • 72 cm²
    • 18 cm²
    • 4 cm²
    • 9 cm²

14. Two similar solids have volumes 8 cm³ and 216 cm³. What is the ratio of their lengths?

    • 1 : 8
    • 1 : 3
    • 1 : 4
    • 1 : 27

15. Two similar triangles have a scale factor of 3. The smaller has area 5 cm². What is the area of the larger?

    • 15 cm²
    • 135 cm²
    • 25 cm²
    • 45 cm²

16. Two similar solids have surface areas 50 cm² and 200 cm². What is the ratio of their lengths?

    • 4 : 1
    • 1 : 4
    • 1 : 2
    • 1 : 16

17. Two similar cones have heights 6 cm and 9 cm. The smaller cone has volume 40 cm³. What is the volume of the larger?

    • 121.5 cm³
    • 90 cm³
    • 60 cm³
    • 135 cm³

18. A room is 6 m by 4 m. It is drawn at a scale of 1 : 50. What is the area of the drawing?

    • 96 cm²
    • 24 cm²
    • 0.96 cm²
    • 480 cm²

19. A box has volume 1000 cm³ and a similar box has volume 8000 cm³. How many times longer are the lengths of the larger box?

    • 3 times
    • 2 times
    • 4 times
    • 8 times

20. A model is built at scale 1 : 20 from a real object of volume 16 m³. What is the volume of the model?

    • 0.8 litres
    • 800 litres
    • 40 litres
    • 2 litres

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