Shape and Space 9

4 marks · Hard

A cuboid has sides of lengths 7 cm, 9 cm, and 15 cm. Calculate the length of the space diagonal (from one corner to the farthest opposite corner), giving your answer to 3 significant figures.

Cuboid: length = 7 cm, width = 9 cm, height = 15 cm; diagonal joins vertex A (0, 0, 0) to vertex F (7, 9, 15).

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18.4 cm (±0.1)

Common mistakes: Missing a squared term; Calculation error

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Marking points

M1 · 1 mark · Correctly identifies need for 3D Pythagoras' theorem (d^2 = l^2 + w^2 + h^2).

M2 · 1 mark · Correctly calculates the length of the base diagonal ().

M3 · 1 mark · Squares and sums all three dimensions correctly.

A1 · 1 mark · Gives the final answer correct to 3 significant figures.

Worked solution

Let the cuboid sides be 7 cm, 9 cm, and 15 cm.

So the length of the space diagonal is 18.4 cm (3 s.f.).