Lesson G19

G19 Lengths, areas and volumes in similar figures Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G19, Lengths, areas and volumes in similar figures: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. Which two conditions must two shapes meet to be congruent?

    • Same size but different shape
    • Same shape and same size
    • Same shape but different size
    • Same perimeter and same area

  2. What does it mean for two shapes to be similar?

    • Same size, with equal corresponding lengths, though the angles may differ in each shape
    • Same perimeter, with corresponding sides equal in length and in the same order
    • Same area, with equal angles but sides in different ratios from one shape to the other
    • Same shape, with equal corresponding angles and corresponding lengths in the same ratio

  3. Two similar triangles have corresponding sides of 3 cm and 12 cm. What is the scale factor from the smaller to the larger?

    • 4
    • 9
    • 0.25
    • 3

  4. A map has scale 1:50 000. A road measures 6 cm on the map. What is its real length?

    • 0.3 km
    • 300 km
    • 3 km
    • 30 km

  5. (H) Two similar shapes have a length scale factor of 5. What is the scale factor for their areas?

    • 125
    • 10
    • 25
    • 5

  6. (H) Two similar solids have a length scale factor of 2. What is the scale factor for their volumes?

    • 6
    • 8
    • 16
    • 4

  7. (H) Two similar prisms have volumes 27 cm^3 and 216 cm^3. What is the length scale factor from the smaller to the larger?

    • 4
    • 8
    • 2
    • 3

  8. (H) Two similar rectangles have areas 9 cm^2 and 36 cm^2. What is the length scale factor from the smaller to the larger?

    • 1.5
    • 3
    • 4
    • 2

  9. (H) A shape is enlarged by a scale factor of 3. Its original area is 5 cm^2. What is the area of the enlargement?

    • 25 cm^2
    • 15 cm^2
    • 45 cm^2
    • 9 cm^2

  10. A model of a bridge is made at scale 1:200. The real bridge is 60 m long. How long is the model?

    • 0.3 cm
    • 300 cm
    • 30 cm
    • 12 cm

  11. (H) Two similar cones have heights 4 cm and 12 cm. What is the ratio of the volume of the larger cone to the volume of the smaller cone?

    • 9 : 1
    • 12 : 1
    • 3 : 1
    • 27 : 1

  12. (H) Two similar shapes have an area scale factor of 49. What is the length scale factor?

    • 24.5
    • 49
    • 14
    • 7

  13. (H) Two similar solids have surface areas 16 cm^2 and 64 cm^2. What is the length scale factor from the smaller to the larger?

    • 2
    • 4
    • 8
    • 1.5

  14. (H) Two similar solids have a volume scale factor of 125. What is the length scale factor?

    • 15
    • 5
    • 25
    • 62.5

  15. (H) Two similar cylinders have a length scale factor of 4. How many times greater is the volume of the larger cylinder?

    • 16
    • 64
    • 8
    • 12

  16. Which set of conditions is NOT enough alone to prove two triangles congruent?

    • ASA
    • SAS
    • SSS
    • AAA

  17. (H) Two similar solids have volumes 135 cm^3 and 40 cm^3. What is the ratio of their corresponding lengths?

    • 27:8
    • 81:16
    • 9:4
    • 3:2

  18. (H) A cylinder of height 10 cm has volume 250 cm^3. A similar cylinder has height 4 cm. What is its volume?

    • 16 cm^3
    • 100 cm^3
    • 40 cm^3
    • 6.25 cm^3

  19. (H) Two similar prisms have surface areas 80 cm^2 and 320 cm^2. The smaller prism has volume 50 cm^3. What is the volume of the larger prism?

    • 400 cm^3
    • 200 cm^3
    • 100 cm^3
    • 1600 cm^3

  20. (H) Two similar shapes have areas in the ratio 49:9. What is the length scale factor from the smaller to the larger?

    • 7/3
    • 49/9
    • 3/7
    • 9/49

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