AQA · Mathematics · 8300

GCSE Maths: Similar shapes: volume

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Similar shapes: volume (Corbettmaths Video 293), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

10 flashcards · Free to study · No account needed

Study this deck

Preparing your cards…

All questions and answers

Read through the full deck, or practise recalling each answer above.

  1. If two shapes are similar with a length scale factor of k, what is the area scale factor?

    Show answer

    k². Areas scale by the square of the length scale factor.

  2. If two similar 3D shapes have a length scale factor of k, what is the volume scale factor?

    Show answer

    k³. Volumes scale by the cube of the length scale factor.

  3. Given two similar shapes with area ratio 4:49, how do you find the length ratio?

    Show answer

    Take the square root of each part of the ratio: √4:√49 = 2:7.

  4. Given two similar 3D shapes with volume ratio 27:1000, how do you find the length ratio?

    Show answer

    Take the cube root of each part of the ratio: ∛27:∛1000 = 3:10.

  5. For similar shapes with length ratio 3:5, the area ratio is ?.

    Show answer

    9:25

  6. If similar shapes have surface area ratio 25:81 and the smaller shape is 30cm long, what is the length of the larger shape?

    Show answer

    54cm. Length ratio is √25:√81 = 5:9, so (30 ÷ 5) × 9 = 54cm.

  7. Why is a claim that a cube with scale factor 3 has 'three times larger' surface area incorrect?

    Show answer

    Because surface area scales by k², not k. The surface area is actually 3² = 9 times larger.

  8. If a toy grows from 4cm to 11cm in height while staying similar, what is the volume scale factor?

    Show answer

    (11/4)³ ≈ 20.8. The volume is approximately 20.8 times larger.

  9. If similar bottles are 12cm and 16cm tall, what fraction of the large bottle's volume does the small bottle contain?

    Show answer

    (12/16)³ = (3/4)³ = 27/64 ≈ 0.42, not 3/4. Volume scales cubically, not linearly.

  10. Given two similar shapes with surface area ratio 2:9, what is their volume ratio?

    Show answer

    First find length ratio: √2:√9 = √2:3. Then cube it for volume: (√2)³:3³ = 2√2:27.

Want to create your own cards? Create a free account. AI generation uses credits.