Shape and Space 9

3 marks · Normal

A cuboid has dimensions 6 cm × 8 cm × 10 cm. Using Pythagoras’ theorem, explain how to find the length of its longest diagonal.

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Use Pythagoras’ theorem for 3D: the space diagonal is cm.

Also accept: By applying Pythagoras’ theorem twice, first for the base and then using the height.; Calculate the diagonal across the base then the diagonal from one corner to the opposite using Pythagoras.

Common mistakes: Only using two sides.

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Marking points

M1 · 1 mark · States/uses the 3D Pythagoras’ theorem or equivalent:

M2 · 1 mark · Correctly substitutes the given lengths: (follow-through)

A1 · 1 mark · Evaluates to cm (3 sf) or exact surd form. (follow-through)

Worked solution

Apply Pythagoras' theorem in 3D. The formula is , where each term is a length of the cuboid.

For 6, 8, 10:

So, the longest diagonal is about 14.1 cm.