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Cambridge IGCSE Maths (0580) · Topic 5: Mensuration · 5.5

Cambridge IGCSE Maths 0580 Compound Shapes Questions

Compound 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 compound shapes →Compound Shapes notes

What the syllabus asks

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

Compound 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 garden plan is a \(12\) m by \(7\) m rectangle with a \(5\) m by \(2\) m rectangle removed from one corner, making an L-shape.
Find (a) the area (b) the perimeter of the L-shape.

Show the worked answer
  1. (a) \(12 \times 7 - 5 \times 2 = 84 - 10 = 74\) m²
  2. (b) Removing a corner rectangle does not change the perimeter: \(2(12 + 7) = 38\) m.

Answer: (a) \(74\) m² (b) \(38\) m

Question 2 Core calculator · easy · 3 marks

A shape is made from a rectangle 12 cm by 6 cm with a semicircle on one of its 6 cm sides. Find the area of the shape. Give your answer correct to 3 significant figures.

Show the answer and mark scheme
  • M1 12 × 6 (= 72)
  • M1 ½ × π × 3² (= 14.13…)
  • A1 86.1 cm²

Answer: \(86.1\text{ cm}^2\)

Question 3 Core calculator · medium

A shape is a rectangle \(12\) cm by \(8\) cm with a semicircle on one of its \(8\) cm sides.
Work out the total area, correct to 3 significant figures.

Show the worked answer
  1. Rectangle: \(96\) cm².
  2. Semicircle of radius \(4\) cm: \(\frac{1}{2} \times \pi \times 16 = 25.13\ldots\) cm².
  3. Total: \(121.13\ldots\) cm²

Answer: \(121\) cm²

Question 4 Core calculator · medium

A circle of radius \(3\) cm is cut out of a square of side \(10\) cm.
Work out the area that is left, correct to 3 significant figures.

Show the worked answer
  1. \(100 - \pi \times 9 = 100 - 28.27\ldots = 71.72\ldots\) cm²

Answer: \(71.7\) cm²

Question 5 Core calculator · medium

A solid is a cuboid \(6\) cm by \(6\) cm by \(4\) cm with a cylinder of radius \(2\) cm and height \(5\) cm fixed on top.
Work out the total volume, correct to 3 significant figures.

Show the worked answer
  1. Cuboid: \(6 \times 6 \times 4 = 144\) cm³.
  2. Cylinder: \(\pi \times 4 \times 5 = 20\pi = 62.83\ldots\) cm³.
  3. Total: \(206.83\ldots\) cm³

Answer: \(207\) cm³

Question 6 Core non-calculator · medium · 2 marks

A cube of edge 4 cm is placed on top of a cuboid measuring 6 cm by 6 cm by 2 cm. Find the total volume of the solid.

Show the answer and mark scheme
  • M1 4³ + 6 × 6 × 2
  • A1 136 cm³

Answer: \(136\text{ cm}^3\)

Question 7 Core calculator · medium · 3 marks

A solid is made from a cylinder of radius 3 cm and height 10 cm with a cone of radius 3 cm and height 4 cm on top. The volume of a cone is \(\frac{1}{3}\pi r^2 h\). Find the total volume. Give your answer correct to 3 significant figures.

Show the answer and mark scheme
  • M1 π × 3² × 10 (= 90π)
  • M1 ⅓ × π × 3² × 4 (= 12π)
  • A1 320 cm³ (320.4…)

Answer: \(320\text{ cm}^3\)

Question 8 Core calculator · hard

A quarter circle has radius \(8\) cm.
Work out its perimeter, correct to 3 significant figures.

Show the worked answer
  1. Arc: \(\frac{1}{4} \times 2\pi \times 8 = 4\pi = 12.56\ldots\) cm.
  2. Add two radii: \(12.56\ldots + 16 = 28.56\ldots\) cm.

Answer: \(28.6\) cm

Compound Shapes questions: Extended

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

Question 9 Extended calculator · hard

A solid hemisphere has radius \(6\) cm.
Work out (a) its volume (b) its total surface area. Give each answer correct to 3 significant figures.

Show the worked answer
  1. (a) Half of \(\frac{4}{3}\pi \times 216\): \(144\pi = 452.3\ldots\) cm³
  2. (b) Curved part: half of \(4\pi r^2 = 72\pi\). Flat circle: \(\pi r^2 = 36\pi\). Total \(108\pi = 339.2\ldots\) cm²

Answer: (a) \(452\) cm³ (b) \(339\) cm²

Question 10 Extended calculator · hard

A cone has base radius \(6\) cm and height \(12\) cm. A small cone of height \(4\) cm and base radius \(2\) cm is cut off the top, leaving a frustum.
Work out the volume of the frustum, correct to 3 significant figures.

Show the worked answer
  1. Large cone: \(\frac{1}{3}\pi \times 36 \times 12 = 144\pi\).
  2. Small cone: \(\frac{1}{3}\pi \times 4 \times 4 = \frac{16}{3}\pi\).
  3. Frustum: \(144\pi - \frac{16}{3}\pi = \frac{416}{3}\pi = 435.6\ldots\) cm³

Answer: \(436\) 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 compound shapes?

Compound Shapes is on both tiers (syllabus 5.5), 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 compound shapes questions?

In the 0580 practice for topic 5 (Mensuration), 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 mensuration questions