Volumes of 3D shapes (Edexcel GCSE Maths): Flashcards

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Volumes of 3D shapes
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Volume formula for a cone

13×base area×vertical height\frac{1}{3} \times \text{base area} \times \text{vertical height}

Volume formula for a circular cone

13πr2h\frac{1}{3}\pi r^2h

Volume formula for a sphere

43πr3\frac{4}{3}\pi r^3

Unique coefficient in sphere volume formula

43\frac{4}{3} (only formula using this)

Volume formula for a pyramid

13×base area×vertical height\frac{1}{3} \times \text{base area} \times \text{vertical height}

Common coefficient in cone & pyramid formulas

13\frac{1}{3}

Best way to express volume answers in exams

Leave in terms of π\pi to avoid rounding errors

Strategy when shapes have equal volumes

Set volume expressions equal, then solve for unknown

What cone volume calculation uses

13\frac{1}{3} of base area × vertical height

Pyramid volume in AhAh notation

13Ah\frac{1}{3}Ah (AA=base area, hh=height)

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