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Worked Examples

Mensuration Worked Examples for IGCSE Maths

Working through solved examples is one of the most effective ways to master mensuration in IGCSE Mathematics. These worked examples, curated by Teacher Rig, cover the most common question types you wi

Working through solved examples is one of the most effective ways to master mensuration in IGCSE Mathematics. These worked examples, curated by Teacher Rig, cover the most common question types you will encounter in the Cambridge IGCSE 0580 exam. Each solution shows every step of working with clear explanations of the reasoning behind each step.

Example 1: Arc length and sector area

Foundation Similar to 0580/22/M/J/22 Q17

Question

A sector has radius 8 cm and angle 120 degrees. Find the arc length and area.

Solution

  1. 1

    Find the arc length

    Arc length = (120/360) x 2 x pi x 8 = (1/3) x 16pi = 16pi/3 = 16.8 cm (3 s.f.)

    Arc length is the fraction of the full circumference.

  2. 2

    Find the sector area

    Area = (120/360) x pi x 8 squared = (1/3) x 64pi = 64pi/3 = 67.0 cm squared (3 s.f.)

    Sector area is the fraction of the full circle area.

Final Answer: Arc length = 16.8 cm, Sector area = 67.0 cm squared

Exam Tip

Both formulas use the same fraction: angle/360. Arc length uses this with 2*pi*r, area uses it with pi*r*r.

Example 2: Volume and surface area of a cylinder

Foundation Similar to 0580/22/O/N/21 Q15

Question

A closed cylinder has radius 5 cm and height 12 cm. Find the volume and total surface area.

Solution

  1. 1

    Find the volume

    V = pi x r squared x h = pi x 25 x 12 = 300pi = 942 cm cubed (3 s.f.)

    Volume = area of circular cross-section x height.

  2. 2

    Find the total surface area

    SA = 2 x pi x r x h + 2 x pi x r squared = 2pi(5)(12) + 2pi(25) = 120pi + 50pi = 170pi = 534 cm squared (3 s.f.)

    Curved surface + two circular ends for a closed cylinder.

Final Answer: Volume = 942 cm cubed, Surface area = 534 cm squared

Exam Tip

For a closed cylinder, remember both circular ends. For an open cylinder (like a pipe), use only one end or none.

Example 3: Volume of a cone and sphere

Extended Similar to 0580/42/M/J/23 Q7

Question

A solid is made of a hemisphere of radius 6 cm attached to a cone of the same radius and height 10 cm. Find the total volume.

Solution

  1. 1

    Find volume of the cone

    V(cone) = (1/3) x pi x 6 squared x 10 = (1/3) x 360pi = 120pi

    V = (1/3) pi r squared h.

  2. 2

    Find volume of the hemisphere

    V(hemisphere) = (2/3) x pi x 6 cubed = (2/3) x 216pi = 144pi

    Hemisphere is half a sphere: (1/2) x (4/3)pi r cubed = (2/3)pi r cubed.

  3. 3

    Add the volumes

    Total = 120pi + 144pi = 264pi = 829 cm cubed (3 s.f.)

    Add the individual volumes for the compound shape.

Final Answer: Total volume = 264pi = 829 cm cubed

Exam Tip

For compound shapes, calculate each part separately then add. Leave answers in terms of pi until the final step for accuracy.

Example 4: Similar shapes and volume scale factor

Extended Similar to 0580/42/O/N/22 Q8

Question

Two similar vases have heights 12 cm and 18 cm. The smaller vase holds 500 ml. Find the capacity of the larger vase.

Solution

  1. 1

    Find the length scale factor

    k = 18/12 = 1.5

    Divide corresponding lengths.

  2. 2

    Find the volume scale factor

    k cubed = 1.5 cubed = 3.375

    Volume scale factor is the cube of the length scale factor.

  3. 3

    Calculate the larger volume

    Volume = 500 x 3.375 = 1687.5 ml

    Multiply the smaller volume by the volume scale factor.

Final Answer: 1687.5 ml or 1688 ml

Exam Tip

Lengths: x k. Areas: x k squared. Volumes: x k cubed. Always identify which type of measurement you are scaling.

Revision Notes

Past Papers

Common Mistakes

Explore Mensuration Subtopics

Area of 2D Shapes Circumference and Area of Circles Arc Length and Sector Area Volume of Prisms and Cylinders Volume of Cones, Spheres, and Pyramids Surface Area Compound Shapes and Solids Similar Shapes (Area and Volume)

Frequently Asked Questions

How many mensuration questions appear in the IGCSE exam?

Mensuration typically appears in both Paper 2 (non-calculator) and Paper 4 (calculator). You can expect 2-4 questions on mensuration across both papers, worth a combined 15-25 marks depending on the session.

What is the best way to practise mensuration for IGCSE?

Start by understanding the methods through worked examples like these, then practise past paper questions under timed conditions. Teacher Rig recommends working through at least 20 mensuration past paper questions before your exam, checking your method against mark schemes.

Should I memorise mensuration formulas for the exam?

Some formulas are given on the formula sheet in the exam, but you should still be very familiar with them. Key formulas that are NOT on the sheet should be memorised. Practice using the formulas so that applying them becomes automatic.

Need Help with Mensuration?

Book a free 60-minute trial class with Teacher Rig. Work through Mensuration problems together and build your confidence.

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