Where can I download free similar shapes (area and vol) PDF worksheets with answers?

On this MathsLinks page you can download free printable similar shapes (area and vol) PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page similar shapes (area and vol) revision guide.

What GCSE grade is similar shapes (area and vol) (6H)?

Similar shapes (area and vol) (topic code 6H) is a Grade 6 geometry topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Similar shapes (area and vol) Worksheets (PDF) with Answers — GCSE Maths

Free Similar shapes (area and vol) PDF Worksheets & Answers

Grade 6 • Topic 6H

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Maths4EveryOne Structured worksheet & solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans

Grade 6 topics
6A - Recurring decimals	6B - Harder indices
6C - The product rule	6D - Repeated change
6E - Triple brackets	6F - Parallel and perpendicular
6G - Inequalities on graphs	6H - Similar shapes (area and vol)
6J - Negative scale factors	6K - Circle theorems
6L - Cumulative frequency	6M - Box plots
6N - Combined transformations	6P - Capture recapture

Explanation:

If two similar shapes have length ratio a : b (scale factor k), then their area ratio is a² : b² (scale factor k²) and their volume ratio is a³ : b³ (scale factor k³).

Whenever you are given two areas or two volumes, always simplify the ratio first and square root (for area) or cube root (for volume) back to the length ratio a : b before finding any other measurement.

Example 1: Similar cylinders A and B have heights 4 cm and 10 cm. The surface area of A is 32 cm². Find the surface area of B.

Solution:

Length ratio = 4 : 10 = 2 : 5 → Area ratio = 2² : 5² = 4 : 25

Area of B = (32 ÷ 4) × 25 = 8 × 25 = 200 cm²

Answer: 200 cm²

Example 2: Similar solids P and Q have surface areas 27 cm² and 75 cm². The volume of Q is 250 cm³. Find the volume of P.

Solution:

Simplify area ratio P : Q = 27 : 75 = 9 : 25 (÷ 3)

Square root for length ratio = 3 : 5

Cube for volume ratio = 3³ : 5³ = 27 : 125

Volume of P = (250 ÷ 125) × 27 = 54 cm³

Answer: 54 cm³

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Similar shapes (area and vol) Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Jun 2025 2H Q16 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

Two jars are mathematically similar.

(a) Work out the height, h cm, of the smaller jar.
Give your answer correct to 1 decimal place. [4 marks]

(b) Find the exact value of p. [1 mark]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Volume scale factor = 1350 ÷ 90 = 15 M3
Linear scale factor = ∛15 ≈ 2.4662. h = 12 ÷ ∛15 = 4.865... ≈ 4.9 cm A1

Answer (a): 4.9 cm

Part (b) Solution:

Area scale factor p = (linear scale factor)² = (∛15)² = 15 {}^2/3) = ∛225 B1

Answer (b): p = 15^2/3 (or ³√(225))

Past Paper Example 2 AQA Nov 2019 2H Q23 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here are three similar cuboids, A, B and C.
A has length 5 cm, width 2 cm and height 3 cm
B has length 10 cm
C has length x cm

(a) The total surface area of A is 62 cm²
Tim wants to work out the total surface area of B.
Here is his working:
10 ÷ 5 = 2
62 × 2 = 124
Total surface area of B = 124 cm²
Make one criticism of Tim's method. [1 mark]

(b) Volume of A × 1258 = Volume of C
Work out the value of x. [3 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

The linear scale factor is 10 ÷ 5 = 2
Surface area scales with the square of the linear scale factor, so the area scale factor is 2² = 4, not 2. C1

Answer (a): He should have multiplied by 2² (4), not 2

Part (b) Solution:

Volume scale factor from A to C = 1258 M1
Linear scale factor = ³√(1258) = 52 = 2.5 M1
Length of A = 5 cm.
x = 5 × 2.5 = 12.5 cm. A1

Answer (b): Answer 12.5

Past Paper Example 3 GCSE Jun 2018 3H Q13 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here are two similar solid shapes.

surface area of shape **A** : surface area of shape **B** = 3 : 4
The volume of shape **B** is 10 cm³
Work out the volume of shape **A**.
Give your answer correct to 3 significant figures.

Worked Solution & Mark Scheme (3 marks)

Length ratio = √3 : √4 = √3 : 2. Volume ratio = (√3)³ : 2³ = 3√3 : 8. Volume of A = 10 × (√3 / 2)³ = 10 × 0.649519 = 6.50 cm³ (3 s.f.). M2 A1

Answer: 6.50 cm³

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