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Updated Mar 11, 2026

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2 pages

Understanding 3D Shapes: Formulas and Examples

Nona

@nona

Three-dimensional shapes are everywhere around you - from the building... Show more

# 3-dimensional shapes

Introduction

3-dimensional shapes have three dimensions: length, width, height.

length

height

width

3-dimension

Understanding 3D Shapes

Every 3D shape has three key measurements: length, width, and height - that's what makes them three-dimensional rather than flat. You'll also need to identify their vertices (corners), edges (lines where faces meet), and faces (flat surfaces).

Think of a cube - it's got 6 square faces, 8 vertices, and 12 edges. Compare that to a cylinder with 3 faces, 0 vertices, and 2 edges, or a cone with 2 faces, 1 vertex, and 1 edge.

Surface area is simply the total area of all faces added together. For a cuboid, you calculate the area of each rectangular face and add them up. Volume tells you how much space is inside the shape.

For cuboids, volume is dead simple: just multiply length × width × height. For other prisms $shapes with the same cross-section throughout$ , multiply the cross-sectional area by the length.

Top Tip: Always check your units - surface area uses cm² whilst volume uses cm³!

Cylinders, Spheres and Formula Learning

Cylinders work just like prisms - find the area of the circular cross-section (πr²) and multiply by the height. Their surface area includes the curved rectangular face plus both circular ends.

Some shapes require you to memorise specific formulas. Don't panic - your exam will often provide these, but knowing them saves time.

Pyramids and cones both use ⅓ in their volume formulas because they taper to a point. Spheres have the most complex formulas, but they follow a pattern with 4π appearing in both volume and surface area calculations.

Plans and elevations are simply 2D drawings showing different views of 3D shapes. The plan shows the bird's-eye view from above, whilst elevations show side views. You can actually reconstruct any 3D shape using these three views.

Exam Strategy: Practice sketching plans and elevations - they're often worth easy marks and help you visualise complex shapes better!

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Updated Mar 11, 2026

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2 pages

Understanding 3D Shapes: Formulas and Examples

Nona

@nona

Three-dimensional shapes are everywhere around you - from the building blocks you played with as a child to the phone in your pocket. Understanding how to calculate their surface area and volume is essential for GCSE maths and surprisingly useful... Show more

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Understanding 3D Shapes

Think of a cube - it's got 6 square faces, 8 vertices, and 12 edges. Compare that to a cylinder with 3 faces, 0 vertices, and 2 edges, or a cone with 2 faces, 1 vertex, and 1 edge.

For cuboids, volume is dead simple: just multiply length × width × height. For other prisms $shapes with the same cross-section throughout$ , multiply the cross-sectional area by the length.

Top Tip: Always check your units - surface area uses cm² whilst volume uses cm³!

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Cylinders, Spheres and Formula Learning

Cylinders work just like prisms - find the area of the circular cross-section (πr²) and multiply by the height. Their surface area includes the curved rectangular face plus both circular ends.

Some shapes require you to memorise specific formulas. Don't panic - your exam will often provide these, but knowing them saves time.

Exam Strategy: Practice sketching plans and elevations - they're often worth easy marks and help you visualise complex shapes better!