Pythagoras in 3D

What you'll learn

1. 1

   Imagine you have a cardboard box — like a shoebox. The longest distance from one corner to the opposite corner, going through the middle, is the 3D diagonal.

2. 2

   The 3D diagonal goes from one corner to the opposite corner. How many corners does a box have?

3. 3

   Let's find the 3D diagonal of a box with sides: length 3 cm, width 4 cm, height 5 cm.

4. 4

   A box has sides: length = 6 cm, width = 8 cm, height = 10 cm. Find the 3D diagonal.

5. 5

   For a box with length = 5, width = 12, height = 13, what is the base diagonal?

6. 6

   Now try this one: a box has length = 2, width = 2, height = 2. Find the 3D diagonal.

7. 7

   What is the 3D diagonal of a cube with side length 5 cm? (Hint: base diagonal = √(5²+5²) = √50)