IGCSE Solid Geometry: Complete Guide for Cambridge IGCSE Mathematics

IGCSE solid geometry is an essential topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering volume and surface area formulas, prisms, cylinders, spheres, and 3D shape calculations is essential for solving geometry problems involving three-dimensional shapes.

This comprehensive IGCSE solid geometry guide covers everything you need to know, including volume and surface area formulas for all common 3D shapes, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know all volume and surface area formulas, how to calculate volumes and surface areas of 3D shapes, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Geometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Solid Geometry Matters

IGCSE solid geometry is an essential topic. Here’s why it’s so important:

• High frequency topic: Solid geometry questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding 3D shapes and their properties
• Exam weight: Typically worth 6-10 marks per paper
• Real-world applications: Used in construction, engineering, and design
• Problem-solving skills: Develops spatial reasoning and formula application abilities

Key insight from examiners: Students often confuse volume and surface area or forget formulas. This guide will help you master all formulas systematically.

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Understanding Solid Geometry

Solid geometry deals with three-dimensional shapes and their properties (volume and surface area).

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Cuboid

Volume = length × width × height Surface area = 2(lw + lh + wh)

Example 1: Cuboid: 5 cm × 4 cm × 6 cm. Find volume and surface area.

Solution: Volume = 5 × 4 × 6 = 120 cm³ Surface area = 2(5×4 + 5×6 + 4×6) = 2(20 + 30 + 24) = 148 cm²

Answer: Volume = 120 cm³, Surface area = 148 cm²

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Cylinder

Volume = πr²h Surface area = 2πr² + 2πrh = 2πr(r + h)

Example 2: Cylinder: radius 4 cm, height 10 cm. Find volume and surface area.

Solution: Volume = π × 4² × 10 = 160π cm³ ≈ 502.65 cm³ Surface area = 2π × 4(4 + 10) = 8π × 14 = 112π cm² ≈ 351.86 cm²

Answer: Volume = 160π cm³, Surface area = 112π cm²

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Sphere

Volume = (4/3)πr³ Surface area = 4πr²

Example 3: Sphere: radius 6 cm. Find volume and surface area.

Solution: Volume = (4/3)π × 6³ = (4/3)π × 216 = 288π cm³ ≈ 904.78 cm³ Surface area = 4π × 6² = 144π cm² ≈ 452.39 cm²

Answer: Volume = 288π cm³, Surface area = 144π cm²

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Prism

Volume = area of cross-section × length Surface area = 2 × area of base + perimeter of base × height

Example 4: Triangular prism: base area 12 cm², length 8 cm, base perimeter 18 cm. Find volume and surface area.

Solution: Volume = 12 × 8 = 96 cm³ Surface area = 2 × 12 + 18 × 8 = 24 + 144 = 168 cm²

Answer: Volume = 96 cm³, Surface area = 168 cm²

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Cone

Volume = (1/3)πr²h Surface area = πr² + πrl (where l = slant height)

Example 5: Cone: radius 5 cm, height 12 cm. Find volume. (Slant height = √(5² + 12²) = 13 cm)

Solution: Volume = (1/3)π × 5² × 12 = 100π cm³ ≈ 314.16 cm³ Surface area = π × 5² + π × 5 × 13 = 25π + 65π = 90π cm² ≈ 282.74 cm²

Answer: Volume = 100π cm³, Surface area = 90π cm²

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Pyramid

Volume = (1/3) × base area × height

Example 6: Square pyramid: base side 6 cm, height 8 cm. Find volume.

Solution: Base area = 6² = 36 cm² Volume = (1/3) × 36 × 8 = 96 cm³

Answer: 96 cm³

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Common Examiner Traps

• Volume vs surface area - Volume = space inside, Surface area = area of all faces
• Formula errors - Learn all formulas clearly
• Units errors - Volume in cubic units, surface area in square units

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Practice Questions

Question 1

Cylinder: radius 3 cm, height 7 cm. Find volume.

Solution: Volume = π × 3² × 7 = 63π cm³ ≈ 197.92 cm³

Answer: 63π cm³

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Tutopiya Advantage: Personalised IGCSE Solid Geometry Coaching

• Live whiteboard walkthroughs of solid geometry problems
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📞 Ready to turn shaky solid geometry skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Solid Geometry

What is the difference between volume and surface area?

Volume is the space inside a 3D shape (cubic units). Surface area is the total area of all faces (square units).

What is the volume of a cylinder?

Volume = πr²h where r is radius and h is height.

What is the volume of a sphere?

Volume = (4/3)πr³ where r is radius.

What is the volume of a cone?

Volume = (1/3)πr²h where r is radius and h is height.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Areas and Perimeters: Complete Guide - Master 2D geometry
• IGCSE Circles: Complete Guide - Master circle properties
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Solid Geometry with Tutopiya

Ready to excel in IGCSE solid geometry? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
• Progress tracking to identify and strengthen weak areas
• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master solid geometry and achieve your target grade.

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