Question 1: Calculate the space diagonal of a cuboid with length 8 cm, width 6 cm, and height 10 cm.

Answer: 12.65

Question 2: A cuboid has a length of 12 cm, a width of 9 cm, and a height of 15 cm. Find the length of its space diagonal.

Answer: 20.52

Question 3: Construct a cuboid with dimensions 5 cm, 7 cm, and 10 cm. Draw its space diagonal on the grid.

Answer: 11.83

Question 4: What is the length of the diagonal of a square base cuboid with side 9 cm and height 12 cm?

Answer: 15

Question 5: A cuboid has a volume of 480 cm³. If its length is 8 cm and width 6 cm, find its height.

Answer: 10

Question 6: A box measures 10 cm by 4 cm by 6 cm. Calculate the surface area of the cuboid.

Answer: 208

Question 7: A cuboid with dimensions 7 cm, 9 cm, and 12 cm is cut diagonally from corner to corner across the face of its base. What is the length of the cut?

Answer: 15

Question 8: Explain how Pythagoras’ theorem applies when finding the space diagonal of a cuboid.

Answer: By applying Pythagoras twice: first to find the diagonal of the base, then using that result with the height to find the space diagonal.

Question 9: A large storage container in the shape of a cuboid has dimensions 3 m by 2 m by 1.5 m. Calculate the length of the space diagonal of the container.

Answer: 3.54

Question 10: A cuboid has a length of 20 cm, width of 15 cm, and a height of 25 cm. Find the length of its space diagonal and verify your answer with Pythagoras' theorem.

Answer: 30

Question 11: A box measures 8 cm by 8 cm by 16 cm. If the diagonal of the base is equal to the height, what is the length of the space diagonal?

Answer: 20