Shape and Space 9

4 marks · Normal

The diagram shows a rectangular box (cuboid) with length 7 cm, width 5 cm and height 12 cm.

Diagram of cuboid ABCDEFGH

Calculate the length of the diagonal from point A to point G (opposite corners of the box). Give your answer correct to 3 significant figures.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

13.9 cm (±0.1)

Also accept: 13.86 cm; 13.86; 13.9

Common mistakes: Using only two dimensions instead of three

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Find the diagonal of the base using Pythagoras' theorem:

M2 · 1 mark · Apply Pythagoras' theorem to the space diagonal using the base diagonal and the height: (follow-through)

A1 · 1 mark · Accurate evaluation of the base diagonal to 1 decimal place or better (follow-through)

A2 · 1 mark · Final answer for AG correct to 3 significant figures and correct unit (follow-through)

Worked solution

First, calculate the diagonal of the base rectangle ABCD.

Now use 3D Pythagoras’ theorem to find the length from A to G (the space diagonal):

Rounding to 3 significant figures: