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Cambridge IGCSE Maths (0580) · Topic 4: Geometry · 4.4

Cambridge IGCSE Maths 0580 Similar Shapes Questions

Similar Shapes questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise similar shapes →Similar Shapes notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Similar Shapes questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

A rectangle \(4\) cm by \(6\) cm is similar to a rectangle \(10\) cm by \(x\) cm, where the \(4\) cm and \(10\) cm sides match.
Find \(x\).

Show the worked answer
  1. Scale factor \(= 10 \div 4 = 2.5\).
  2. \(x = 6 \times 2.5 = 15\)

Answer: \(x = 15\)

Question 2 Core calculator · easy · 2 marks

A photo is 12 cm wide and 8 cm high. It is enlarged so that its width is 30 cm. Find its new height.

Show the answer and mark scheme
  • M1 30 ÷ 12 = 2.5
  • A1 20 cm

Answer: \(20\) cm

Question 3 Core non-calculator · medium

Triangle \(ABC\) is similar to triangle \(PQR\), with \(A\) matching \(P\), \(B\) matching \(Q\) and \(C\) matching \(R\).
\(AB = 6\) cm, \(BC = 8\) cm, \(PQ = 9\) cm and \(PR = 15\) cm.
Find (a) \(QR\) (b) \(AC\).

Show the worked answer
  1. Scale factor from \(ABC\) to \(PQR\): \(9 \div 6 = 1.5\).
  2. (a) \(QR = 8 \times 1.5 = 12\) cm
  3. (b) \(AC = 15 \div 1.5 = 10\) cm

Answer: (a) \(12\) cm (b) \(10\) cm

Question 4 Core calculator · medium

A \(2\) m post casts a shadow \(1.5\) m long. At the same time a tree casts a shadow \(9\) m long.
How tall is the tree?

Show the worked answer
  1. The triangles are similar. Scale factor \(= 9 \div 1.5 = 6\).
  2. Tree \(= 2 \times 6 = 12\) m

Answer: \(12\) m

Question 5 Core non-calculator · medium · 3 marks

In triangle \(ABC\), \(D\) is on \(AB\) and \(E\) is on \(AC\), and \(DE\) is parallel to \(BC\). \(AD = 4\) cm, \(AB = 10\) cm and \(DE = 6\) cm. Find \(BC\).

Show the answer and mark scheme
  • M1 triangles ADE and ABC are similar
  • M1 6 × 10/4
  • A1 15 cm

Answer: \(15\) cm

Question 6 Core calculator · medium · 2 marks

Two bottles are similar. Their heights are 18 cm and 27 cm. The diameter of the base of the smaller bottle is 6.4 cm. Find the diameter of the base of the larger bottle.

Show the answer and mark scheme
  • M1 27 ÷ 18 = 1.5
  • A1 9.6 cm

Answer: \(9.6\) cm

Question 7 Core non-calculator · hard

In triangle \(ABC\), \(D\) is on \(AB\) and \(E\) is on \(AC\), with \(DE\) parallel to \(BC\). \(AD = 4\) cm, \(DB = 6\) cm and \(DE = 5\) cm.
Find \(BC\).

Show the worked answer
  1. Triangles \(ADE\) and \(ABC\) are similar. \(AB = 4 + 6 = 10\) cm.
  2. Scale factor \(= 10 \div 4 = 2.5\), so \(BC = 5 \times 2.5 = 12.5\) cm.

Answer: \(12.5\) cm

Similar Shapes questions: Extended

Extended content, for Papers 2 and 4. Core students can skip these.

Question 8 Extended non-calculator · medium

Two similar shapes have lengths in the ratio \(2 : 5\). The smaller shape has an area of \(12\) cm².
Find the area of the larger shape.

Show the worked answer
  1. Area ratio \(= 2^2 : 5^2 = 4 : 25\).
  2. \(12 \times \frac{25}{4} = 75\) cm²

Answer: \(75\) cm²

Question 9 Extended calculator · hard

Two similar bottles have heights \(10\) cm and \(15\) cm. The smaller bottle holds \(400\) cm³.
How much does the larger bottle hold?

Show the worked answer
  1. Length scale factor \(= 1.5\), so volume scale factor \(= 1.5^3 = 3.375\).
  2. \(400 \times 3.375 = 1350\) cm³

Answer: \(1350\) cm³

Question 10 Extended calculator · hard

Two similar solids have surface areas of \(50\) cm² and \(200\) cm². The larger solid has a volume of \(640\) cm³.
Find the volume of the smaller solid.

Show the worked answer
  1. Area scale factor \(= 4\), so length scale factor \(= 2\) and volume scale factor \(= 8\).
  2. \(640 \div 8 = 80\) cm³

Answer: \(80\) cm³

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test similar shapes?

Similar Shapes is on both tiers (syllabus 4.4), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more similar shapes questions?

In the 0580 practice for topic 4 (Geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More geometry questions