AQA · Mathematics · 8300
GCSE Maths: Pythagoras: 3D
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Pythagoras: 3D (Corbettmaths Video 259), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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In a cube with side length s, what is the formula for the length of the diagonal across one face?
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s√2, found by applying Pythagoras' theorem to two sides of length s.
In a cube with side length s, what is the formula for the space diagonal (vertex to opposite vertex)?
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s√3, found by applying Pythagoras' theorem twice: first to find the face diagonal (s√2), then using that with the third edge.
In a cuboid with dimensions a, b, and c, what is the formula for the space diagonal?
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√(a² + b² + c²), found by applying Pythagoras' theorem in 3D.
How many applications of Pythagoras' theorem are typically needed to find a space diagonal in a 3D shape?
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Two applications: first to find a diagonal in a 2D face, then using that diagonal with the third dimension to find the space diagonal.
In a cube with side length 4cm, the space diagonal AG has length ? cm.
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4√3
To determine if a rod will fit inside a box, what measurement should you calculate?
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The space diagonal of the box (longest possible straight line inside), then compare it to the rod's length.
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