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Similar shapes: area & volume practice questions with answers

Higher · Grade 6 · Calculator

A second set of similar shapes: area & volume questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Length scale factor 6. What is the area scale factor?

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Answer: 36

  1. Area scale is k^2.
  2. 6^2 = 36.
  • Method (1): Area scale is k^2.
  • Accuracy (1): 6^2 = 36.

Question 2 Easy

Length scale factor 2. What is the area scale factor?

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Answer: 4

  1. Area scale is k^2.
  2. 2^2 = 4.
  • Method (1): Area scale is k^2.
  • Accuracy (1): 2^2 = 4.

Question 3 Medium

Length scale factor 5. What is the volume scale factor?

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Answer: 125

  1. Volume scale is k^3.
  2. 5^3 = 125.
  • Method (1): Volume scale is k^3.
  • Accuracy (1): 5^3 = 125.

Question 4 Medium

Length scale factor 1. What is the volume scale factor?

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Answer: 1

  1. Volume scale is k^3.
  2. 1^3 = 1.
  • Method (1): Volume scale is k^3.
  • Accuracy (1): 1^3 = 1.

Question 5 Hard

Volume scale factor 8. What is the length scale factor?

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Answer: 2

  1. Length scale is cube root.
  2. Cube root of 8 is 2.
  • Method (1): Length scale is cube root.
  • Accuracy (1): Cube root of 8 is 2.

Question 6 Hard

Volume scale factor 64. What is the length scale factor?

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Answer: 4

  1. Length scale is cube root.
  2. Cube root of 64 is 4.
  • Method (1): Length scale is cube root.
  • Accuracy (1): Cube root of 64 is 4.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Length scale factor 6. What is the volume scale factor?

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Answer: 216

  1. Volume scale factor is the cube of the length scale factor: 6 × 6 × 6.
  2. 6 × 6 = 36, then 36 × 6 = 216.
  • Method (1): Cubes the length scale factor: 6^3 or 6 × 6 × 6
  • Accuracy (1): Final answer 216

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Area scale from a length scale uses which power?

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The square. The square.

Check 2

Square the length: length scale factor 3. The area scale factor is

  1. area scale is 25
  2. volume scale is 27
  3. area scale is 9
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area scale is 9 3^2 = 9.

Check 3

Square the length: length scale factor 4. The area scale factor is

  1. area scale is 9
  2. area scale is 16
  3. area scale is 25
Show answer

area scale is 16 4^2 = 16.

Check 4

Volume scale from a length scale uses which power?

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The cube. The cube.

Check 5

Cube the length: length scale factor 2. The volume scale factor is

  1. volume scale is 8
  2. area scale is 25
  3. area scale is 9
Show answer

volume scale is 8 2^3 = 8.

Check 6

Cube the length: length scale factor 3. The volume scale factor is

  1. volume scale is 27
  2. area scale is 9
  3. volume scale is 8
Show answer

volume scale is 27 3^3 = 27.

Check 7

Area scale factor 9. What is the length scale factor?

  1. length scale is 3
  2. length scale is 5
  3. length scale is 2
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length scale is 3 √9 = 3.

Check 8

Area scale factor 25. What is the length scale factor?

  1. length scale is 3
  2. length scale is 5
  3. length scale is 2
Show answer

length scale is 5 √25 = 5.

Check 9

Volume scale factor 8. What is the length scale factor?

  1. length scale is 2
  2. length scale is 3
  3. length scale is 5
Show answer

length scale is 2 Cube root of 8 is 2.

Check 10

Volume scale factor 27. What is the length scale factor?

  1. length scale is 2
  2. length scale is 3
  3. length scale is 5
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length scale is 3 Cube root of 27 is 3.

Check 11

Why is the area scale not equal to the length scale?

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Area grows in two directions. Area grows in two directions.

Check 12

Why cube a length scale for volume?

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Volume grows in three directions. Volume grows in three directions.

Check 13

Square root returns you from an area scale to a

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Length scale. Length scale.

Check 14

Cube root returns you from a volume scale to a

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Length scale. Length scale.

Check 15

Length scale factor 5. The area scale factor is

  1. volume scale is 27
  2. volume scale is 8
  3. area scale is 25
Show answer

area scale is 25 5^2 = 25.

Keep going with Similar shapes: area & volume

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