Finding the long diagonal of a cuboid

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

A cuboid is 6 cm by 8 cm by 24 cm. What is its long diagonal in cm?
Answer: ______________
A cuboid is 3 cm by 4 cm by 12 cm. What is its long diagonal?
- 12
- 19
- 13
- 5
A cuboid is 3 cm by 4 cm by 12 cm. What is its long diagonal?
- 5 cm
- 13 cm
- 12 cm
Aisha says the long diagonal of a cuboid needs Pythagoras twice. Is Aisha right?
Circle one: True False
A cuboid is 9 cm by 12 cm by 8 cm. What is its long diagonal in cm?
Answer: ______________
Sam drew no sketch and treated 12 as a short side. What should Sam have done?
- Redrawn the triangle flat with the right angle marked
- Added all three edges
- Measured the angle first
What is the best first step for a cuboid diagonal?
- Find the base diagonal
- Add the three edges
- Measure an angle
- Find the volume
Aisha says the space diagonal of a cuboid needs Pythagoras twice. Is Aisha right?
Circle one: True False
A pyramid has vertical height 8 cm and centre to corner distance 6 cm. What is the lateral edge?
- 10 cm
- 14 cm
- 48 cm
A cuboid is 7 cm by 24 cm by 60 cm. What is its long diagonal in cm?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

26 · Base 10, then root of 100 plus 576 = 26.
13 · Base diagonal 5, then upright triangle gives root of 25 plus 144 = 13. The 5 option stops after step one.
13 cm · Base diagonal 5 cm first, then the upright triangle gives 13 cm.
True · Once for the base diagonal, once for the upright triangle.
17 · Base 15, then root of 225 plus 64 = 17.
Redrawn the triangle flat with the right angle marked · A flat sketch with the hypotenuse labelled stops side mix ups.
Find the base diagonal · The base diagonal plus the height forms the upright triangle that holds the space diagonal.
True · Once for the base diagonal, once for the upright triangle.
10 cm · Root of 64 plus 36 is 10. Adding the sides gives 14.
65 · Base 25, then root of 625 plus 3600 = 65.