Similar Shapes: Area and Volume Scale Factors · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Big copy, bigger area

Mathematics · Geometry · ages 14-15
Name ______________________   Date ____________

  1. A photo 4 cm by 5 cm is enlarged with length scale factor 3. What is the area of the enlargement in cm²?

    Answer: ______________

  2. Two similar shapes have length scale factor 3. By what do you multiply an area?

    • 3
    • 6
    • 9

  3. A solid is enlarged with length scale factor 2. By what do you multiply its volume? Give the number.

    Answer: ______________

  4. Doubling every length of a solid doubles its volume.

    Circle one:   True   False

  5. Two similar solids have volumes in ratio 8:1, larger to smaller. What is the length scale factor?

    Answer: ______________

  6. Two similar jugs are 10 cm and 15 cm tall. How many times more does the taller one hold? Give the number.

    Answer: ______________

  7. A photo 4 cm by 5 cm is enlarged with length scale factor 3. What is the area of the enlargement in cm squared?

    Answer: ______________

  8. Two similar shapes have length scale factor 4. The smaller area is 5 cm². What is the larger area?

    • 80 cm²
    • 20 cm²
    • 40 cm²
    • 100 cm²

  9. Two similar solids have volumes in ratio 27 to 1, larger to smaller. What is the length scale factor? Give the number.

    Answer: ______________

  10. Two similar shapes have areas in ratio 25 to 1, larger to smaller. What is the length scale factor?

    • 25
    • 12.5
    • 5
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Big copy, bigger area W1-mt_v37c_AeLQa-s1

  1. 180 · The original area is 20 and areas scale by 3 squared = 9, so 180.
  2. 9 · Areas scale by k squared, and 3 squared is 9.
  3. 8 · The volume factor is 2 cubed, which is 8.
  4. False · Volumes scale by 2 cubed, which is 8, not 2.
  5. 2 · The cube root of 8 is 2.
  6. 3.375 · The length factor is 1.5 and 1.5 cubed is 3.375.
  7. 180 · The old area is 20 and areas scale by 9, so 180.
  8. 80 cm² · Areas scale by 4 squared = 16, and 5 × 16 = 80.
  9. 3 · The length ratio is the cube root of 27, which is 3.
  10. 5 · The length ratio is the square root of 25, which is 5.
Worksheet · LightMySky